Question

Is 392 a perfect cube? If not, find smallest natural number by which 392 must be multiplied so that the product is a perfect cube ?​

Answer 1

Answer:

392 is not a perfect cube.

prime factorization of 392 =2*2*2*7*7

So there are a pair of 2 but not of 7.

So to make a 392 a perfect cube we will multiply the number by 7.

Answer 2

Answer:

Therefore, 392 is not a perfect cube. To make its a cube, we need one more 7. In that case 392 × 7 = 2 × 2 × 2 × 7 × 7 × 7 = 2744 which is a perfect cube. Hence the smallest natural number by which 392 should be multiplied to make a perfect cube is 7.