Question

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

Answer 1

Answer:

No, 392 is not a perfect cube.

The number 7 should be multiplied by 392 so that the product is a perfect cube, because 392×7= 2744 which is a cube root of 14.

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Answer 2

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• 392 = 2 × 2 × 2 × 7 × 7

• The prime factor 7 does not appear in a group of three. 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.