Question

by what number 88209 be divided so that the quotient is a perfect cube? Find the number. Also find the cube root of the product.​

Answer 1

Step-by-step explanation:

To find the smallest number by which 88209 must be divided so that the quotient is a perfect cube, we have to find the prime factors of 88209.

88209=3×3×3×3×3×3×11×11

Prime factors of 88209 are 3,3,3,3,3,3,11,11.

Out of the prime factors of 88209, 11 cannot be considered in its perfect cube as it have only two factors of 11.

So, 11×11 is the number by which 88209 must be divided to make the quotient a perfect cube.

⇒

11×11

88209

=729

3

729

=9

Hence, the smallest number is 121, which when divides 88209, the quotient is 729 which is a perfect cube.

Hence, the correct answer is 121.