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

$\huge\underline\mathrm{SOLUTION:-}$

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 2³ x 7³ or 14³.

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

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Answer 2

Step-by-step explanation:

329 is not a perfect cube.

By prime factorizing 329, you will get

329= 7×47

So, 329 should be multiplied by 7×7 and 47×47 to make it a perfect cube.....

Hope this helps u....

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