Book: NCERT - Mathematics
Chapter: 7. Cubes and Cube Roots
Subject: Maths - Class 8th
Q. No. 1 of Exercises 7.2
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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
(i) Prime factorization of 64 is as follows:
= 2 x 2 x 2 x 2 x 2 x 2
Hence,
= 4
(ii) Prime factorization of 512 is as follows:
= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
Hence,
= 8
(iii) Prime factorization of 10648 is as follows:
= 2 x 2 x 2 x 11 x 11 x 11
Hence,
= 22
(iv) Prime factorization of 27000 is as follows:
= 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 x 5
Hence,
= 30
(v) Prime factorization of 15625 is as follows:
= 5 x 5 x 5 x 5 x 5 x 5
Hence,
= 25
(vi) Prime factorization of 13824 is as follows:
= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3
Hence,
= 24
(vii) Prime factorization of 110592 is as follows:
= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3
Hence,
= 48
(viii) Prime factorization of 46656 is as follows:
= 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3
Hence,
= 36
(ix) Prime factorization of 175616 is as follows:
= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 7 x 7 x 7
Hence,
= 56
(x) Prime factorization of 91125 is as follows:
= 3 x 3 x 3 x 3 x 3 x 3 x 5 x 5 x 5
Hence,
= 45