Squares And Square Roots

square root of 289 = 17

∴ square root of 289 = 17

Step 1: Place a bar over every pair of digits starting from the one’s digit

Step 2: Find the largest number whose square is ≤ the number under the extreme left bar (1² < 2 < 2²). Take this number as the divisor and the quotient with number under extreme left bar as the dividend.

Divide and get the remainder. (1in this case)

Step 3. Bring down the number under the next bar(i.e.,89 in this case)to the right of the remainder. So the new dividend is 189

Step 4. Double the divisor and place this digit at ten’s place of new divisor (1 +1 in this case)

Step 5. Guess the largest possible digit to fill the unit’s digit of new divisor which also become the new digit in the quotient, such that new divisor is multiplied to the new quotient the product is ≤ the dividend.

In this case 47 × 7 = 189. Get the remainder.

Step 6. Since the remainder is 0 and no digits are left in the given number.

∴ = 17

Square root of 2025 = 45

∴ square root of 2025 = 45

Step 1: Place a bar over every pair of digits starting from the one’s digit

Step 2: Find the largest number whose square is ≤ the number under the extreme left bar (4² < 20 < 5²). Take this number as the divisor and the quotient with number under extreme left bar as the dividend. Divide and get the remainder. (4 in this case)

Step 3. Bring down the number under the next bar(i.e.,25 in this case) to the right of the remainder. So the new dividend is 425

Step 4. Double the divisor and place this digit at ten’s place of new divisor (4+4 in this case)

Step 5. Guess the largest possible digit to fill the unit’s digit of new divisor which also become the new digit in the quotient, such that new divisor is multiplied to the new quotient the product is ≤ the dividend.

In this case 85 × 5 = 425. Get the remainder.

Step 6. Since the remainder is 0 and no digits are left in the given number.

∴ = 45

Square root of 64009 = 253

∴ Square roots of 64009 = 253

Step 1: Place a bar over every pair of digits starting from the one’s digit

Step 2: Find the largest number whose square is ≤ the number under the extreme left bar (2² < 6 < 3²). Take this number as the divisor and the quotient with number under extreme left bar as the dividend.

Divide and get the remainder. (2 in this case)

Step 3. Bring down the number under the next bar(i.e.,40 in this case) to the right of the remainder. So the new dividend is 240.

Step 4. Double the divisor and place this digit at ten’s place of new divisor (2+2 in this case)

Step 5. Guess the largest possible digit to fill the unit’s digit of new divisor which also become the new digit in the quotient, such that new divisor is multiplied to the new quotient the product is ≤ the dividend.

In this case 45 × 5 = 225. Get the remainder.

Step 6. Double the divisor once again and place this digit at ten’s place of new divisor (45+5 in this case)

Step 7. Guess the largest possible digit to fill the unit’s digit of new divisor which also become the new digit in the quotient, such that new divisor is multiplied to the new quotient the product is ≤ the dividend.

In this case 503 × 3 = 1509. Get the remainder

Step 8. Since the remainder is 0 and no digits are left in the given number.

∴ = 17

Square root of 646416 = 804

∴ square root of 646416 = 804

Step 1: Place a bar over every pair of digits starting from the one’s digit

Step 2: Find the largest number whose square is ≤ the number under the extreme left bar (8² < 64 < 9²). Take this number as the divisor and the quotient with number under extreme left bar as the dividend. Divide and get the remainder(0 in this case).

Step 3. Bring down the number under the next bar(i.e.,64 in this case) to the right of the remainder. So the new dividend is 064.

Step 4. Double the divisor and place this digit at ten’s place of new divisor (8+8 in this case)

Step 5. Guess the largest possible digit to fill the unit’s digit of new divisor which also become the new digit in the quotient, such that new divisor is multiplied to the new quotient the product is ≤ the dividend.

In this case 160 × 0 = 0. Get the remainder.

Step 6. Double the divisor once again and place this digit at ten’s place of new divisor (160+0in this case)

Step 7. Guess the largest possible digit to fill the unit’s digit of new divisor which also become the new digit in the quotient, such that new divisor is multiplied to the new quotient the product is ≤ the dividend.

In this case 1604 × 4 = 6416. Get the remainder

Step 8. Since the remainder is 0 and no digits are left in the given number.

∴ = 804

(1) 3 × 3 = 9

∴3 is square root of 9

(-3) × (-3) = 9

∴ (-3) is also the square root of 9

Thus, 3 & -3 are two square roots of 9

(2) 5 × 5 = 25

∴5 is square root of 25

(-5) × (-5) = 25

∴ (-5) is also the square root of 25

Thus, 5 & -5 are two square roots of 25

(3) 10 × 10 = 100

∴10 is square root of 100

(-10) × (-10) = 100

∴ (-10) is also the square root of 100

Thus, 10 & -10 are two square roots of 100

(4) 14 × 14 = 196

∴14 is square root of 196

(-14) × (-14) = 196

∴ (-14) is also the square root of 196

Thus, 14 & -14 are two square roots of 196

(5) 18 × 18 = 324

∴18 is square root of 324

(-18) × (-18) = 324

∴ (-18) is also the square root of 324

Thus, 18 & -18 are two square roots of 324

(6) 24 × 24 = 524

∴24 is square root of 524

(-24) × (-24) = 524

∴ (-24) is also the square root of 524

Thus, 24 & -24 are two square roots of 524

(1) : Positive square root of 324

(2) - : Negative square root of 324

(3) - : Negative square root of 625

(4) : Positive square root of 625

(1) The positive square root of 400: →

(2) The negative square root of 81: → -

(3) The negative square root of 121: → -

(4) The positive square root of 1: →

(1)
⇒


(2)

⇒

(4)

⇒

In ∆ABC, AB = 5cm, BC = 7cm ∠B = 90°

By Pythagoras theorem

AC² = AB² + BC²

= (5)² + (7)²

= 25 + 49

= 74

Hence, AC² = 74

∴ AC =

In ∆ABC, AB = 12cm, BC = 7cm ∠B = 90°

By Pythagoras theorem

AC² = AB² + BC²

= (12)² + (7)²

= 144 + 49

= 193

Hence, AC² = 193

∴ AC =

In ∆ABC, AB = 8cm, BC = 8cm ∠B = 90°

By Pythagoras theorem

AC² = AB² + BC²

= (8)² + (8)²

= 64 + 64

= 128

Hence, AC² = 128

∴ AC =

Square root of 10 = 3.1622

Third decimal place = 3.162

Second decimal place = 3.16

One decimal place = 3.1

Step 1: Place a bar over every pair of digits starting from the one’s digit

Step 2: Find the largest number whose square is ≤ the number under the extreme left bar (3² < 10 < 4²). Take this number as the divisor and the quotient with number under extreme left bar as the dividend. Divide and get the remainder.(1in this case)

Step 3. Bring down the number under the next bar(i.e.,00 in this case) to the right of the remainder. So the new dividend is 100. Put a decimal in the quotient.

Step 4. Double the divisor and place this digit at ten’s place of new divisor (3+3 in this case)

Step 5. Guess the largest possible digit to fill the unit’s digit of new divisor which also become the new digit in the quotient, such that new divisor is multiplied to the new quotient the product is ≤ the dividend.

In this case 626 × 6 = 3756. Get the remainder.

Step 6. Double the divisor and place this digit at ten’s place of new divisor (626+6 in this case)

Step 7. Guess the largest possible digit to fill the unit’s digit of new divisor which also become the new digit in the quotient, such that new divisor is multiplied to the new quotient the product is ≤ the dividend.

In this case 6322 × 2 = 12644. Get the remainder.

Step 8. Double the divisor and place this digit at ten’s place of new divisor (6322+2 in this case)

Step 9. Guess the largest possible digit to fill the unit’s digit of new divisor which also become the new digit in the quotient, such that new divisor is multiplied to the new quotient the product is ≤ the dividend.

In this case 63242 × 2 = 126484. Get the remainder.

Step 10. Since the remainder is 49116 and we were required to calculate the square root till 4^th decimal place.

∴ = 3.1622

Square root of 135 = 11.6189

Third decimal place = 11.619 (round figure of 11.618)

Second decimal place = 11.62 (round figure of 11.61)

One decimal place = 11.6

Step 1: Place a bar over every pair of digits starting from the one’s digit

Step 2: Find the largest number whose square is ≤ the number under the extreme left bar (1² < 1 < 2²). Take this number as the divisor and the quotient with number under extreme left bar as the dividend. Divide and get the remainder.(0 in this case)

Step 3. Bring down the number under the next bar(i.e.,35 in this case) to the right of the remainder. So the new dividend is 35.

Step 4. Double the divisor and place this digit at ten’s place of new divisor (1+1 in this case)

Step 5. Guess the largest possible digit to fill the unit’s digit of new divisor which also become the new digit in the quotient, such that new divisor is multiplied to the new quotient the product is ≤ the dividend.

In this case 21 × 1 = 21. Get the remainder.

Step 6. Bring down the number under the next bar(i.e.,00 in this case) to the right of the remainder. So the new dividend is 1400. Put a decimal in quotient.

Step 7. Double the divisor and place this digit at ten’s place of new divisor (21+1 in this case).

Step 8. Guess the largest possible digit to fill the unit’s digit of new divisor which also become the new digit in the quotient, such that new divisor is multiplied to the new quotient the product is ≤ the dividend.

In this case 226 × 6 = 1356. Get the remainder.

Step 9. Bring down the number under the next bar(i.e.,00 in this case) to the right of the remainder. So, new dividend is 4400

Step 10. Double the divisor and place this digit at ten’s place of new divisor (226+6 in this case)

Step 11. Guess the largest possible digit to fill the unit’s digit of new divisor which also become the new digit in the quotient, such that new divisor is multiplied to the new quotient the product is ≤ the dividend.

In this case 2321 × 1 = 2321. Get the remainder.

Step 12. Bring down the number under the next bar(i.e.,00 in this case) to the right of the remainder. So the new dividend is 207900

Step 13. Double the divisor and place this digit at ten’s place of new divisor (2321+1 in this case).

Step 14. Guess the largest possible digit to fill the unit’s digit of new divisor which also become the new digit in the quotient, such that new divisor is multiplied to the new quotient the product is ≤ the dividend.

In this case 23228 × 8 = 185824. Get the remainder.

Step 15. Bring down the number under the next bar(i.e.,00 in this case) to the right of the remainder. So the new dividend is 2207600

Step 13. Double the divisor and place this digit at ten’s place of new divisor (23228+8 in this case). 116279

Step 14. Guess the largest possible digit to fill the unit’s digit of new divisor which also become the new digit in the quotient, such that new divisor is multiplied to the new quotient the product is ≤ the dividend.

In this case 232369 × 9 = 2091321. Get the remainder.

Step 10. Since the remainder is 116279 and we were required to calculate the square root till 4^th decimal place.

∴ = 11.6189

Square root of 777 = 27.8747

Third decimal place = 27.875 (round figure of 27.874)

Second decimal place = 27.88 (round figure of 27.87)

One decimal place = 27.9 (round figure of 27.8)

Step 1: Place a bar over every pair of digits starting from the one’s digit

Step 2: Find the largest number whose square is ≤ the number under the extreme left bar (2² < 7 < 3²). Take this number as the divisor and the quotient with number under extreme left bar as the dividend. Divide and get the remainder.(3 in this case)

Step 3. Bring down the number under the next bar(i.e.,77 in this case)to the right of the remainder. So the new dividend is 377.

Step 4. Double the divisor and place this digit at ten’s place of new divisor (2+2 in this case)

Step 5. Guess the largest possible digit to fill the unit’s digit of new divisor which also become the new digit in the quotient, such that new divisor is multiplied to the new quotient the product is ≤ the dividend.

In this case 47 × 7 Get the remainder.

Step 6. Bring down the number under the next bar(i.e.,00 in this case) to the right of the remainder. So the new dividend is 4800. Put a decimal in quotient.

Step 7. Double the divisor and place this digit at ten’s place of new divisor (47+7 in this case).

Step 8. Guess the largest possible digit to fill the unit’s digit of new divisor which also become the new digit in the quotient, such that new divisor is multiplied to the new quotient the product is ≤ the dividend.

In this case 548 × 8 = 4384. Get the remainder.

Step 9. Bring down the number under the next bar(i.e.,00 in this case) to the right of the remainder. So, new dividend is 41600

Step 10. Double the divisor and place this digit at ten’s place of new divisor (548+8in this case)

Step 11. Guess the largest possible digit to fill the unit’s digit of new divisor which also become the new digit in the quotient, such that new divisor is multiplied to the new quotient the product is ≤ the dividend.

In this case 5567 × 7 = 38969. Get the remainder.

Step 12. Bring down the number under the next bar(i.e.,00 in this case) to the right of the remainder. So the new dividend is 263100

Step 13. Double the divisor and place this digit at ten’s place of new divisor (5567+7 in this case).

Step 14. Guess the largest possible digit to fill the unit’s digit of new divisor which also become the new digit in the quotient, such that new divisor is multiplied to the new quotient the product is ≤ the dividend.

In this case 55744 × 4 = 222976. Get the remainder.

Step 15. Bring down the number under the next bar(i.e.,00 in this case) to the right of the remainder. So the new dividend is 4012400

Step 16. Double the divisor and place this digit at ten’s place of new divisor (55744+4 in this case).

Step 17. Guess the largest possible digit to fill the unit’s digit of new divisor which also become the new digit in the quotient, such that new divisor is multiplied to the new quotient the product is ≤ the dividend.

In this case 557487 × 7 = 3902409 Get the remainder.

Step 18. Since the remainder is 109991 and we were required to calculate

the square root till 4^th decimal place.

∴ = 27.8747

Square root of 1000 = 31.6227

Third decimal place = 31.623 (round figure of 31.622)

Second decimal place = 31.62

One decimal place = 31.6

Step 1: Place a bar over every pair of digits starting from the one’s digit

Step 2: Find the largest number whose square is ≤ the number under the extreme left bar (3² < 10 < 4²). Take this number as the divisor and the quotient with number under extreme left bar as the dividend. Divide and get the remainder.(1 in this case)

Step 3. Bring down the number under the next bar(i.e.,00 in this case) to the right of the remainder. So the new dividend is 100.

Step 4. Double the divisor and place this digit at ten’s place of new divisor (3+3 in this case)

Step 5. Guess the largest possible digit to fill the unit’s digit of new divisor which also become the new digit in the quotient, such that new divisor is multiplied to the new quotient the product is ≤ the dividend.

In this case 61 × 1 = 61. Get the remainder.

Step 6. Bring down the number under the next bar (i.e.,00 in this case) to the right of the remainder. So the new dividend is 3900. Put a decimal in quotient.

Step 7. Double the divisor and place this digit at ten’s place of new divisor (61+1 in this case).

Step 8. Guess the largest possible digit to fill the unit’s digit of new divisor which also become the new digit in the quotient, such that new divisor is multiplied to the new quotient the product is ≤ the dividend.

In this case 626 × 6 = 3756. Get the remainder.

Step 9. Bring down the number under the next bar (i.e.,00 in this case) to the right of the remainder. So, new dividend is 14400

Step 10. Double the divisor and place this digit at ten’s place of new divisor (626+6 in this case)

Step 11. Guess the largest possible digit to fill the unit’s digit of new divisor which also become the new digit in the quotient, such that new divisor is multiplied to the new quotient the product is ≤ the dividend.

In this case 6322 × 2 = 12644. Get the remainder.

Step 12. Bring down the number under the next bar(i.e.,00 in this case) to the right of the remainder. So the new dividend is 175600

Step 13. Double the divisor and place this digit at ten’s place of new divisor (6322+2 in this case).

Step 14. Guess the largest possible digit to fill the unit’s digit of new divisor which also become the new digit in the quotient, such that new divisor is multiplied to the new quotient the product is ≤ the dividend.

In this case 63242 × 2 = 126484. Get the remainder.

Step 15. Bring down the number under the next bar (i.e.,00 in this case) to the right of the remainder. So the new dividend is 4911600

Step 16. Double the divisor and place this digit at ten’s place of new divisor (63242+2 in this case).

Step 17. Guess the largest possible digit to fill the unit’s digit of new divisor which also become the new digit in the quotient, such that new divisor is multiplied to the new quotient the product is ≤ the dividend.

In this case 632447 × 7 = 4427129. Get the remainder.

Step 18. The remainder is 484471 , since, we were required to calculate the square root till 4^th decimal place.

∴ = 31.6227

Square root of 5328 = 72.9931

Third decimal place = 72.993

Second decimal place = 72.99

One decimal place = 73.0(round figure of 72.9)

Step 1: Place a bar over every pair of digits starting from the one’s digit

Step 2: Find the largest number whose square is ≤ the number under the extreme left bar (7² <53< 8²). Take this number as the divisor and the quotient with number under extreme left bar as the dividend. Divide and get the remainder.(4 in this case)

Step 3. Bring down the number under the next bar(i.e.,28 in this case)to the right of the remainder. So the new dividend is 428.

Step 4. Double the divisor and place this digit at ten’s place of new divisor (7+7 in this case)

Step 5. Guess the largest possible digit to fill the unit’s digit of new divisor which also become the new digit in the quotient, such that new divisor is multiplied to the new quotient the product is ≤ the dividend.

In this case 142 × 2 = 284. Get the remainder.

Step 6. Bring down the number under the next bar(i.e.,00 in this case) to the right of the remainder. So the new dividend is 14400. Put a decimal in quotient.

Step 7. Double the divisor and place this digit at ten’s place of new divisor (142+2 in this case).

Step 8. Guess the largest possible digit to fill the unit’s digit of new divisor which also become the new digit in the quotient, such that new divisor is multiplied to the new quotient the product is ≤ the dividend.

In this case 1449 × 9 = 13041. Get the remainder.

Step 9. Bring down the number under the next bar(i.e.,00 in this case) to the right of the remainder. So, new dividend is 135900

Step 10. Double the divisor and place this digit at ten’s place of new divisor (1449+9 in this case)

Step 11. Guess the largest possible digit to fill the unit’s digit of new divisor which also become the new digit in the quotient, such that new divisor is multiplied to the new quotient the product is ≤ the dividend.

In this case 14589 × 9 = 131301. Get the remainder.

Step 12. Bring down the number under the next bar(i.e.,00 in this case) to the right of the remainder. So the new dividend is 459900

Step 13. Double the divisor and place this digit at ten’s place of new divisor (14589+9 in this case).

Step 14. Guess the largest possible digit to fill the unit’s digit of new divisor which also become the new digit in the quotient, such that new divisor is multiplied to the new quotient the product is ≤ the dividend.

In this case 145983 × 3 = 439749. Get the remainder.

Step 15. Bring down the number under the next bar (i.e.,00 in this case) to the right of the remainder. So the new dividend is 2195100

Step 16. Double the divisor and place this digit at ten’s place of new divisor (145983+3 in this case).

Step 17. Guess the largest possible digit to fill the unit’s digit of new divisor which also become the new digit in the quotient, such that new divisor is multiplied to the new quotient the product is ≤ the dividend.

In this case 1459861 × 1 = 1459861. Get the remainder.

Step 18. The remainder is 735239, since, we were required to calculate the square root till 4^th decimal place.

∴ = 72.9931

Square root of 56.25 = 7.5

(1): To find the square root of a decimal number we put bars on the integral part(i.e.,56) of the number in the usual manner. And place

bars on the decimal part (i.e.,25) on every pair of digits beginning with the first decimal place. .

(2): Find the largest number whose square is ≤ the number under the extreme left bar (7² <56< 8²). Take this number as the divisor and the quotient with number under extreme left bar as the dividend. Divide and get the remainder.( 7 in this case)

(3): The remainder is 7. Write the number under the next bar(i.e.,25) to the right of this remainder to get, 725

(4): Double the divisor and place this digit at ten’s place of new divisor (7+7 in this case).

(5): We know that 145 × 5 = 725, ∴ the new digit is 5.

Divide and get the remainder.

(6): Since the remainder is 0 and no bar is left,

∴ = 7.5

Square root of 151.29 = 12.3

(1): To find the square root of a decimal number we put bars on the integral part(i.e.,151) of the number in the usual manner. And place bars on the decimal part (i.e.,29) on every pair of digits beginning with the first decimal place. .

(2): Find the largest number whose square is ≤ the number under the extreme left bar (1² <1< 2²). Take this number as the divisor and the quotient with number under extreme left bar as the dividend. Divide and get the remainder.

(3): The remainder is 0. Write the number under the next bar(i.e.,51) to the right of this remainder to get, 51

(4): Double the divisor and place this digit at ten’s place of new divisor (1+1 in this case).

(5): We know that 22 × 2 = 44, ∴ the new digit is 2.

Divide and get the remainder.

(6): The remainder is 7. Write the number under the next bar(i.e.,29) to the right of this remainder to get, 729

(7): Double the divisor and place this digit at ten’s place of new divisor (22+2in this case).

(8): We know that 243 × 3 = 729, ∴ the new digit is 3.

Divide and get the remainder.

(9): Since the remainder is 0 and no bar is left,

∴ = 12.3

Square root of 49.5616 = 7.04

(1): To find the square root of a decimal number we put bars on the integral part(i.e.,49) of the number in the usual manner. And place

bars on the decimal part (i.e.,5616) on every pair of digits beginning with the first decimal place. .

(2): Find the largest number whose square is ≤ the number under the extreme left bar (7² <49< 8²). Take this number as the divisor and the quotient with number under extreme left bar as the dividend. Divide and get the remainder.

(3): The remainder is 0. Write the number under the next bar(i.e.,56) to the right of this remainder to get, 56

(4): Double the divisor and place this digit at ten’s place of new divisor (7+7 in this case).

(5): We know that 140 × 0 = 0, ∴ the new digit is 0.

Divide and get the remainder.

(6): The remainder is 56. Write the number under the next bar(i.e.,16) to the right of this remainder to get, 5616

(7): Double the divisor and place this digit at ten’s place of new divisor (140+0in this case).

(8): We know that 1404 × 4 = 5616, ∴ the new digit is 4.

Divide and get the remainder.

(9): Since the remainder is 0 and no bar is left,

∴ = 7.04

Square root of 443.5236

(1): To find the square root of a decimal number we put bars on the integral part(i.e.,443) of the number in the usual manner. And place bars on the decimal part (i.e.,5236) on every pair of digits beginning with the first decimal place. .

(2): Find the largest number whose square is ≤ the number under the extreme left bar (2² <4<3²). Take this number as the divisor and the quotient with number under extreme left bar as the dividend. Divide and get the remainder.

(3): The remainder is 0. Write the number under the next bar(i.e.,43) to the right of this remainder to get, 43

(4): Double the divisor and place this digit at ten’s place of new divisor (2+2 in this case).

(5): We know that 41 × 1 = 41, ∴ the new digit is 1.

Divide and get the remainder.

(6): The remainder is 2. Write the number under the next bar(i.e.,52) to the right of this remainder to get, 252

(7): Double the divisor and place this digit at ten’s place of new divisor (41+1in this case).

(8): We know that 420 × 0 = 0, ∴ the new digit is 0.

Divide and get the remainder.

(6): The remainder is 252. Write the number under the next bar(i.e.,36) to the right of this remainder to get, 25236

(7): Double the divisor and place this digit at ten’s place of new divisor (420+0 in this case).

(8): We know that 4206 × 6 = 25236, ∴ the new digit is 6.

Divide and get the remainder.

(9): Since the remainder is 0 and no bar is left,

∴ = 21.06

Square root of 59.03 to second decimal place = 7.68

(1): To find the square root of a decimal number we put bars on the integral part(i.e.,59) of the number in the usual manner. And place bars on the decimal part (i.e.,03) on every pair of digits beginning with the first decimal place. .

(2): Find the largest number whose square is ≤ the number under the extreme left bar (7² <59< 8²). Take this number as the divisor and the quotient with number under extreme left bar as the dividend. Divide and get the remainder.( 10 in this case)

(3): The remainder is 10. Write the number under the next bar(i.e.,03) to the right of this remainder to get, 1003

(4): Double the divisor and place this digit at ten’s place of new divisor (7+7 in this case).

(5): We know that 146 × 6 = 876, ∴ the new digit is 6.

Divide and get the remainder.

(6): The remainder is127. Write the number under the next bar(i.e.,00) to the right of this remainder to get, 12700

(7): Double the divisor and place this digit at ten’s place of new divisor (146+6 in this case).

(8): We know that 1528 × 8 = 1224, ∴ the new digit is 6.

Divide and get the remainder.

(9): The remainder is 476 and we are required to calculate till second decimal place.

∴ = 7.68

Square root of 3.4158 to second decimal place 1.85

(1): To find the square root of a decimal number we put bars on the integral part(i.e.,3) of the number in the usual manner. And place bars on the decimal part (i.e.,4158) on every pair of digits beginning with the first decimal place. .

(2): Find the largest number whose square is ≤ the number under the extreme left bar (1² <3< 2²). Take this number as the divisor and the quotient with number under extreme left bar as the dividend. Divide and get the remainder.( 2 in this case)

(3): The remainder is 2. Write the number under the next bar(i.e.,41) to the right of this remainder to get, 241

(4): Double the divisor and place this digit at ten’s place of new divisor (1+1 in this case).

(5): We know that 28 × 8 = 224, ∴ the new digit is 8.

Divide and get the remainder.

(6): The remainder is 17. Write the number under the next bar(i.e.,58) to the right of this remainder to get, 1758

(7): Double the divisor and place this digit at ten’s place of new divisor (28+8 in this case).

(8): We know that 364 × 4 = 1456, ∴ the new digit is 4.

Divide and get the remainder.

(9): The remainder is 302 and we are required to calculate till second decimal place.

∴ = 1.84

Square root of 34.158 to second decimal place = 5.84

(1): To find the square root of a decimal number we put bars on the integral part(i.e.,34) of the number in the usual manner. And place bars on the decimal part (i.e.,158) on every pair of digits beginning with the first decimal place. .

(2): Find the largest number whose square is ≤ the number under the extreme left bar (5² <34< 6²). Take this number as the divisor and the quotient with number under extreme left bar as the dividend. Divide and get the remainder.( 9 in this case)

(3): The remainder is 9. Write the number under the next bar(i.e.,51) to the right of this remainder to get, 951

(4): Double the divisor and place this digit at ten’s place of new divisor (5+5 in this case).

(5): We know that 108 × 8 = 864, ∴ the new digit is 8.

Divide and get the remainder.

(6): The remainder is51. Write the number under the next bar(i.e.,80) to the right of this remainder to get,5180

(7): Double the divisor and place this digit at ten’s place of new divisor (108+8 in this case).

(8): We know that 1164 × 4 = 4656, ∴ the new digit is 4.

Divide and get the remainder.

(9): The remainder is 524 and we are required to calculate till second decimal place.

∴ = 5.84

Square root of 720.5 to second decimal place = 26.84

(1): To find the square root of a decimal number we put bars on the integral part(i.e.,720) of the number in the usual manner. And place bars on the decimal part (i.e.,50) on every pair of digits beginning with the first decimal place. .

(2): Find the largest number whose square is ≤ the number under the extreme left bar (2² <7< 3²). Take this number as the divisor and the quotient with number under extreme left bar as the dividend. Divide and get the remainder.(3 in this case)

(3): The remainder is 3. Write the number under the next bar(i.e.,20) to the right of this remainder to get, 320

(4): Double the divisor and place this digit at ten’s place of new divisor (2+2 in this case).

(5): We know that 46 × 6 = 276, ∴ the new digit is 6.

Divide and get the remainder.

(6): The remainder is 44. Write the number under the next bar(i.e.,50) to the right of this remainder to get, 4450

(7): Double the divisor and place this digit at ten’s place of new divisor (46+6 in this case).

(8): We know that 528 × 8 = 4224, ∴ the new digit is 8.

Divide and get the remainder.

(9): The remainder is 226. Write the number under the next bar(i.e.,00) to the right of this remainder to get, 22600

(10): Double the divisor and place this digit at ten’s place of new divisor (528+8 in this case).

(11): We know that 5364 × 4 = 21456, ∴ the new digit is 4.

Divide and get the remainder.

(12): The remainder is 1144 and we are required to calculate till second decimal place.

∴ = 26.84