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Find the smallest number by which 675 must be divided to obtain a perfect cube.

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Find the smallest number by which 675 must be divided to obtain a perfect cube.

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We find that 675 = 3 x 3 x 3 x 5 x 5

= 3 x 3 x 3 x 5 x 5

Here we have an ungrouped 5 x 5.

So if we divide 675 by 5 x 5 then the new number will be a perfect cube.

ie. 675 ÷ 25 = 27

The new number is 27

3√27 = 3√3 x 3 x 3 = 3

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