Question

Find the smallest number by which 5184 should be multiplied so that the product is a perfect cube .
(give full method )
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Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

Given number is 5184

On prime factorising of 5184, we get

5184=2×2×2×2×2×2×3×3×3×3

After grouping the same kind of prime factors is 3’s, its seen that one factor 3 is left ungroup.

5184=(2×2×2)×(2×2×2)×(3×3×3)×3

So, in order to complete it in 3’s, we must multiply the factors 3×3 i.e. equal to 9.

Thus, the required smallest number that should be multiplied to 5184 so that product is a perfect cube is 9.

And,

The cube root of 5184×9=46656 is

=2×2×3×3=36.

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