Cubes And Cube Roots
Class 8th Mathematics (old) MHB Solution
- 6^3 Find the values.
- (-5)^3 Find the values.
- (-10)^3 Find the values.
- 14^3 Find the values.
- (-12)^3 Find the values.
Exercise 45
Question 1.Evaluate the following and write which number is the cube of which other number.
(1) 33 (2) 73
(3) 43 (4) 93
(5) 113 (6) 153
Answer:
(1) The cube of 3 can be written as follows:
⟹ 3 × 3 × 3
⟹ 9 × 3
= 27
Hence 33 = 27.
(2) The cube of 7 can be written as follows:
⟹ 7 × 7 × 7
⟹ 49 × 7
= 343
Hence 73 = 343.
(3) The cube of 4 can be written as follows:
⟹ 4 × 4 × 4
⟹ 16 × 4
= 64
Hence 43 = 64.
(4) The cube of 9 can be written as follows:
⟹ 9 × 9 × 9
⟹ 81 × 9
= 729
Hence 93 = 729.
(5) The cube of 11 can be written as follows:
⟹ 11 × 11 × 11
⟹ 121 × 11
= 1331
Hence 113 = 1331.
(6) The cube of 15 can be written as follows:
⟹ 15 × 15 × 15
⟹ 225 × 15
= 3375
Hence 153 = 3375.
Exercise 46
Question 1.Find the values.
63
Answer:
Since the number is a positive one, no need to worry about the sign of the final value.
The cube of 6 can be written as follows:
⟹ 6 × 6 × 6
⟹ 36 × 6
= 216
Hence 63 = 216.
Question 2.
Find the values.
(–5)3
Answer:
Here the number is negative.
So during multiplication care has to be taken of the sign.
The basic rules are:
Negative Number × Negative Number = Positive
Negative Number × Positive Number = Negative Number
Positive Number × Positive Number = Positive Number
The cube of -5 can be written as follows:
⟹ -5 × -5 × -5
⟹ 25 × -5
= -125
Hence (-5)3 = -125
Question 3.
Find the values.
(–10)3
Answer:
Here the number is negative.
So during multiplication care has to be taken of the sign.
The basic rules are:
Negative Number × Negative Number = Positive
Negative Number × Positive Number = Negative Number
Positive Number × Positive Number = Positive Number
The cube of -10 can be written as follows:
⟹ -10 × -10 × -10
⟹ 100 × -10
= -1000
Hence (-10)3 = -1000
Question 4.
Find the values.
143
Answer:
Since the number is a positive one, no need to worry about the sign of the final value.
The cube of 14 can be written as follows:
⟹ 14 × 14 × 14
⟹ 196 × 14
= 2744
Hence 143 = 2744.
Question 5.
Find the values.
(–12)3
Answer:
Here the number is negative.
So during multiplication care has to be taken of the sign.
The basic rules are:
Negative Number × Negative Number = Positive
Negative Number × Positive Number = Negative Number
Positive Number × Positive Number = Positive Number
The cube of -5 can be written as follows:
⟹ -12 × -12 × -12
⟹ 144 × -12
= -1728
Hence (-12)3 = -1728
Exercise 47
Question 1.Write in symbols.
(1) The cube root of 64 is 4.
(2) The cube root of -1000 is -10.
(3) The cube root of -1 is -1.
(4) The cube root of 8000 is 20.
Answer:
(1) The symbol of cube root of any number is as follows:
The representation of the above is as follows:
In words it can be interpreted as the cube root of 64 is equal to 4.
(2) The symbol of cube root of any number is as follows:
The representation of the above is as follows:
In words it can be interpreted as the cube root of -1000 is equal to -10.
(3) The symbol of cube root of any number is as follows:
The representation of the above is as follows:
In words it can be interpreted as the cube root of -1 is equal to -1.
(4) The symbol of cube root of any number is as follows:
The representation of the above is as follows:
In words it can be interpreted as the cube root of 8000 is equal to 20.
Question 2.
Write in words.
(1) 
(2) 
(3) 
(4) 
Answer:
(1) The symbolic notation can be interpreted as follows:
Here 
means cube root of -512.
So total meaning of the notation is,
Cube root of -512 is -8
(2) The symbolic notation can be interpreted as follows:
Here 
means cube root of 1.
So total meaning of the notation is,
Cube root of 1 is 1
(3) The symbolic notation can be interpreted as follows:
Here 
means cube root of 729.
So total meaning of the notation is,
Cube root of 729 is 9.
(4) The symbolic notation can be interpreted as follows:
Here 
means cube root of -729.
So total meaning of the notation is,
Cube root of -729 is -9.
Exercise 48
Question 1.Write the cubes of the natural numbers from 1 to 10.
Answer:
The cube of 1 can be written as follows:
⟹ 1 × 1 × 1
⟹ 1 × 1
= 1
Hence 13 = 1.
The cube of 2 can be written as follows:
⟹ 2 × 2 × 2
⟹ 4 × 2
= 8
Hence 23 = 8.
The cube of 3 can be written as follows:
⟹ 3 × 3 × 3
⟹ 9 × 3
= 27
Hence 33 = 27.
The cube of 4 can be written as follows:
⟹ 4 × 4 × 4
⟹ 16 × 4
= 64
Hence 43 = 64.
The cube of 5 can be written as follows:
⟹ 5 × 5 × 5
⟹ 25 × 5
= 125
Hence (5)3 = 125
The cube of 6 can be written as follows:
⟹ 6 × 6 × 6
⟹ 36 × 6
= 216
Hence 63 = 216.
The cube of 7 can be written as follows:
⟹ 7 × 7 × 7
⟹ 49 × 7
= 343
Hence 73 = 343.
The cube of 8 can be written as follows:
⟹ 8 × 8 × 8
⟹ 64 × 8
= 512
Hence 83 = 512.
The cube of 9 can be written as follows:
⟹ 9 × 9 × 9
⟹ 81 × 9
= 729
Hence 93 = 729.
The cube of 10 can be written as follows:
⟹ 10 × 10 × 10
⟹ 100 × 10
= 1000
Hence (10)3 = 1000
Question 2.
Find the cube roots of the following numbers.
(1) -729
(2) 8000
(3) 2744
(4) 6859
Answer:
(1) Here,
729 = 9 × 81
= 9 × 9 × 9
Therefore
Therefore
(2) Here,
8000 = 20 × 400
= 20 × 20 × 20
Therefore
(3) Here,
2744 = 14 × 196
= 14 × 14 × 14
Therefore 
(4) Here,
6859 = 19 × 361
= 19 × 19 × 19
Therefore 
Question 3.
Of which numbers are the following numbers, the cubes?
(1) 4096
(2) 4913
(3) 5832
(4) -2197
Answer:
(1) Here,
(2) Here,
(3) Here,
(4) Here,
So 