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

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