Find 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

Solution:

To find the cube root of a number, the factors in the prime factorization of the number should be grouped as triplets.

(i) 64

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

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Video Solution:

Find 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

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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