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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.

 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.

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5861 Points
6 months ago
Dear Student

The prime factorisation of 392 gives:

392 = 2 x 2 x 2 x 7 x 7

Since, we can see, number 7 cannot be paired in a group of three. Therefore, 392 is not a perfect cube.

To make it a perfect cube, we have to multiply the 7 by the original number.

Thus,

2 x 2 x 2 x 7 x 7 x 7 = 2744, which is a perfect cube, such as 2^3x 7^3or 14^3.

Hence, the smallest natural number which should be multiplied to 392 to make a perfect cube is 7.

Thanks

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