Question

by which smallest natural number 392 must be multiplied so as to make the product a perfect cube?

Answer 1

Prime factorisation of 392:

392 = 2³ x 7²

.

To get a perfect cube, all exponents must be in the multiples of 3.

Let k be the smallest number to be multiplied to 392 to get a perfect cube:

392k = 2³ x 7³

392 = 2³ x 7²

k = 7¹ = 7

.

Answer: The number is 7

Answer 2

392=7*7*2*2*2

so it should be multiplied to 7

2744=$(14)^{3}$