Question

Check whether the following numbers are perfect cubes. (a) 6675 (b) 1728 (c) 157464

Answer 1

Answer:

(a) 6675

Prime Factorization = 3*5*5*89

Since there are no triplets of numbers in the prime Factorization , therefore 6675 is NOT a PERFECT CUBE .

(b)1728

Prime Factorization= 2*2*2*2*2*2*3*3*3

=(2)^3 * (2)^3 *(3)^3

Since we need perfect cube and the numbers are in triplets or they are forming cube , thus , 1728 is A PERFECT CUBE .

(c)157464

Prime Factorization=2^3 *3^3 * 3^3 * 3^3

As all the numbers are in triplets or they are forming cubes , thus 157464 is A PERFECT CUBE.

Answer 2

(a) 6675

Prime Factorization = 3*5*5*89

Since there are no triplets of numbers in the prime Factorization , therefore 6675 is NOT a PERFECT CUBE .

(b)1728

Prime Factorization= 2*2*2*2*2*2*3*3*3

=(2)^3 * (2)^3 *(3)^3

Since we need perfect cube and the numbers are in triplets or they are forming cube , thus , 1728 is A PERFECT CUBE .

(c)157464

Prime Factorization=2^3 *3^3 * 3^3 * 3^3

As all the numbers are in triplets or they are forming cubes , thus 157464 is A PERFECT CUBE.