Question

"Question 1 Find the cube root of each of the following numbers by prime factorisation method. (i) 64 (ii) 512 (iii) 10648 (iv) 27000 (v) 15625 (vi) 13824 (vii) 110592 (viii) 46656 (ix) 175616 (x) 91125

Class 8 Cubes and Cube Roots Page 116"

Answer 1

To find the cube root by prime factorization:

In the prime factorization of a perfect cube the factors can be grouped such that is group contains 3 equal prime factors.

Hence, to find the cube root of perfect cube say  n , proceed as follows:

 

1. Find the prime factors of a given number n

2.Form groups of 3 factors such that all three factor in each group are equal.

3.Choose one factor from each group and find the product . This product is the required cube root.

 

If a group contains one or two equal factor only then a given number cannot be a perfect cube.

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Solution:

[ prime factorization is in the attachments]

i)  64 = 2 x 2 x 2 x 2 x 2 x 2
= 2³ x 2³
³√64 =   2×2=4

ii) 512 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
= 2³x 2³ x 2³
³√512 =   2×2×2=8

iii)  10648 = 2 x 2 x 2 x 11 x 11 x 11
= 2³ x 11³
³√10648 =   2×11=22

iv)  27000 = 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 x 5
= 2³ x 3³ x 5³
³√27000 =   2×3×5=30

v) 15625 = 5 x 5 x 5 x 5 x 5 x 5
= 5³x 5³
³15625 =   5×5=25

vi) 13824 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3
= 2³x 2³ x 2³ x 3³
³√13824 =   2×2×2×3=24

vii) 110592 = 2³ x 2³ x 2³ x 2³ x 3³
³√110592 =   2×2×2×2×3=48


viii) 46656 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3
= 2³ x 2³ x 3³x 3³
³√46656 =   2×2×3×3=36

ix) 175616 = 2³x 2³ x 2³ x 7³
³√175616 =   2×2×2×7=56

x) 91125 = 5³ x 3³ x 3³
³√91125 =   5×3×3=45

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Hope this will help you...

Answer 2

Answer:

1. 64=4
2. 513=8
3. 10648=22
4. 27000=30
5. 15625=25
6. 13824=24
7. 110592=48
8. 46656=36
9. 175616=56
10. 91125=45