 # NCERT Solutions for Class 8 Maths Chapter 7:Cube roots CBSE Part 1

In this page we have NCERT book Solutions for Class 8 Maths Chapter 7:cube roots for EXERCISE 1 . Hope you like them and do not forget to like , social share and comment at the end of the page.
Question 1
Which of the following numbers are not perfect cubes?
(i) 216
.(ii) 128
(iii) 1000
(iv) 100
(v) 46656
i) Converting the number into common factors
216 = 2 x 2 x 2 x 27
= 2 x 2 x 2 x 3 x 3 x 3
As number of 2s and 3s is 3 in the factorization so it is a perfect cube
Therefore
3√216 =  2×3=6
ii) 128 = 2 x 2 x 2 x 2 x 2 x 2 x 2
Number of 2s is 7 and 7 is not divisible by three so 128 is not a perfect cube
iii) 1000 = 2 x 2 x 2 x 5 x 5 x 5
Number of 2s and 5s is 3 each so 1000 is a perfect cube.
Therefore
3√1000 =  2×5=10
iv) 100 = 2 x 2 x 5 x 5
Number of 2s and 5s is 2 each and not 3 so 100 is not a perfect cube.
v) 46656
= 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3
Number of 2s and 3s is 6 each and 6 is divisible by 3 so 46656 is a perfect cube
Therefore
3√46656=  2×2×3×3=36
Question 2
Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube.
(i) 243
(ii) 256
(iii) 72
(iv) 675
(v) 100

Converting the number into common factors
i) 243 = 3 x 3 x 3 x 3 x 3
Number of 3s is 5, so we need to another 3 in the factorization to make 243 a perfect cube. 243 multiplied by 3 will be a perfect cube.
ii) 256 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
Number of 2s is 8 so 256 needs to be multiplied by 2 to become a perfect cube.
iii) 72 = 2 x 2 x 2 x 3 x 3
Number of 2s is 3 and that of 3s is 2, so 72 needs to be multiplied by 3 to become a perfect cube.
iv)  675 = 5 x 5 x 27 = 5 x 5 x 3 x 3 x 3
675 needs to be multiplied by 5 to become a perfect cube.
v) 100 = 10 x 10
100 needs to be multiplied by 10 to become a perfect cube.
Question 3
Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube.
(i) 81
(ii) 128
(iii) 135
(iv) 192
(v) 704
Converting the number into common factors
i) 81 = 3 x 3 x 3 x 3
So we have 4 3’s,Therefore
81 needs to be divided by 3 to become a perfect cube.
ii) 128 = 2 x 2 x 2 x 2 x 2 x 2 x 2
So we have 7 2’s,Therefore
128 needs to be divided by 2 to become a perfect cube.
iii) 135 = 5 x 3 x 3 x 3
So we have 1 5’s and 3 3’s Therefore
135 needs to be divide by 5 to become a perfect cube.
iv) 192 = 2 x 2 x 2 x 2 x 2 x 2 x 3
So we have 6 2’s and 1 3’s Therefore
192 needs to be divided by 3 to become a perfect cube.
v) 704 = 2 x 2 x 2 x 2 x 2 x 2 x 11
So we have 6 2’s and 1 11’s Therefore
704 needs to be divided by 11 to become a perfect cube.
Question 4
Parikshit makes a cuboid of plasticine of sides 5 cm, 2 cm, 5 cm. How many such cuboids will he need to form a cube?
Answer: The volume of the cuboid =2×5×5 cm3
If we multiply this expression by 2×2×5, The it become perfect cube.
Now Volume of cube is given by
=a3 where a is the side of the cube
So that means we need  2×2×5=20 cuboid to make the cube