 # 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

Reference Books for class 8 Math

Given below are the links of some of the reference books for class 8 Math.

1. Mathematics Foundation Course for JEE/Olympiad : Class 8 This book can take students maths skills further. Only buy if child is interested in Olympiad/JEE foundation courses.
2. Mathematics for Class 8 by R S Aggarwal Detailed Mathematics book to clear basics and concepts. I would say it is a must have book for class 8 student.
3. Pearson Foundation Series (IIT -JEE / NEET) Physics, Chemistry, Maths & Biology for Class 8 (Main Books) | PCMB Combo : These set of books could help your child if he aims to get extra knowledge of science and maths. These would be helpful if child wants to prepare for competitive exams like JEE/NEET. Only buy if you can provide help to the child while studying.
4. Reasoning Olympiad Workbook - Class 8 :- Reasoning helps sharpen the mind of child. I would recommend students practicing reasoning even though they are not appearing for Olympiad.

You can use above books for extra knowledge and practicing different questions.

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