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:

2 | 392

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2 | 196

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2 | 98

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7 | 49

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**** 7

392 = 2 × 2 × 2 × 7 × 7

The Prime factor 7 doesn't appear in a group of three factors.

So, 392 is not a perfect cube .

Hence, the smallest number by which it is be multiplied to make it a perfect cube is 7.

Now,

392 × 7 = 2 × 2 × 2 × 7 × 7 × 7

Answer 2

Answer:

.  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.