Question

Is 292 a perfect cube? If not find the smallest natural number by which it must be multiplied so that the product is a perfect cube. (

Answer 1

Find the Prime Factor:

292 = 2² x 73

Is 292 a perfect cube:

⇒ 292 is NOTa perfect cube.

⇒ A perfect cube requires its prime factors to have exponents that are a multiple of 3s.

Define k:

Let k the smallest natural number which 292 needs to multiply to be a perfect cube.

Solve k:

292 = 2² x 73

292k = 2³ x 73³

Therefore k = 2 x 73² = 10658

Answer: The number is 10658

Answer 2

2² x 73...........................