Answer
64 = 2 × 2 × 2 × 2 × 2 × 2
= 23 × 23
∛64 = 2 × 2 = 4
(ii) 512
512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
= 23 × 23 × 23
∛512 = 2 × 2 × 2 = 8
(iii) 10648
10648 = 2 × 2 × 2 × 11 × 11 × 11
= 23 × 113
∛10648 = 2 × 11 = 22
(iv) 27000
27000 = 2 × 2 × 2 × 3 × 3 × 3 × 5 × 5 × 5
= 23 × 33 × 53
∛27000 = 2 × 3 × 5 = 30
(v) 15625
15625 = 5 × 5 × 5 × 5 × 5 × 5
= 53 × 53
∛15625 = 5 × 5 = 25
(vi) 13824
13824 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3
= 23 × 23 × 23 × 33
∛13824 = 2 × 2 × 2 × 3 = 24
(vii) 110592
110592 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3
= 23 × 23 × 23 × 23 × 33
∛110592 = 2 × 2 × 2 × 2 × 3 = 48
(viii) 46656
46656 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3
= 23 × 23 × 33 × 33
∛46656 = 2 × 2 × 3 × 3 = 36
(ix) 175616
175616 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 7 × 7 × 7
= 23 × 23 × 23 × 73
∛175616 = 2 × 2 × 2 × 7 = 56
(x) 91125
91125 = 5 × 5 × 5 × 3 × 3 × 3 × 3 × 3 × 3
= 53 × 33 × 33
∛91125 = 5 × 3 × 3 = 45
☛ Check: NCERT Solutions for Class 8 Maths Chapter 7
Video Solution:
NCERT Solutions for Class 8 Maths Chapter 7 Exercise 7.2 Question 1
Summary:
The cube root of each of the following numbers by prime factorization method. (i) 64 (ii) 512 (iii) 10648 (iv) 27000 (v) 15625 (vi) 13824 (vii) 110592 (viii) 46656 (ix) 175616 (x) 91125 are (i) 4, (ii) 8, (iii) 22, (iv) 30, (v) 25, (vi) 24, (vii) 48, (viii) 36, (ix) 56, (x) 45
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Example 7 Find the cube root of 13824 by prime factorisation method. We see that, 13824 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 Since 2 & 3 occur in triplets ∴ 13824 is a perfect cube Cube root of 13824 = 2 × 2 × 2 × 3 = 4 × 6 = 24