Question

find the smallest number by which 339 must be multiplied so that the product is a perfect cube. also find the cube root of the perfect cube so obtained

Answer 1

The smallest number is 114921 and the cube root of the result is 339

Explanation:

The number 339 can be factored as:

339 = 3 * 113

Both factors are prime, thus to produce a perfect cube, we must multiply by each factor to the power of 2, that is:

3^2*113^2=114921

When we multiply 339 by 114921 we get 38958219, a perfect cube which cube root is 339.

Thus, the smallest number is 114921 and the cube root of the result is 339