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in Squares And Square Roots by (50.4k points)
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By what smallest number should 3600 be multiplied so that the quotient is a perfect cube. Also find the cube root of the quotient.

1 Answer

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by (49.8k points)
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Best answer

Factors of 3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5

Now, grouping the prime factors = (2 × 2 × 2) × 2 × 3 × 3 × 5 × 5

Factors 2, 3 and 5 has no pair.

∴3600 is not a perfect cube.

The smallest number it should be multiplied to get a perfect cube is 2 × 2 × 3 × 5 = 60

Then,

Product = 3600 × 60 = 216000

Factors of 21600 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5 × 5 × 5

3√216000

3√(23 × 23 × 33 × 53)

= 2 × 2 × 3 × 5

= 60

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