Question

By what smallest number should 9000 be divided so that the quotient is a perfect cube. Find the cube root of the quotient. with proccedure

Answer 1

Resolving 9000 into prime factors, we get

2 | 9000

________

2 | 4500

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2 | 2250

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3 | 1125

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3 | 375

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5 | 125

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5 | 25

________

**** 5

9000 = 2×2×2× 3×3 × 5×5×5

The prime factor 3 doesn't appear in a group of three factors .

So, 9000 is not a perfect cube.

Hence, the smallest number which is to be divided to make it perfect cube is 3× 3= 9.

$\orange {Perfect \:cube } = \frac{9000}{9}$

= 2×2×2× 5×5×5

= ( 2 × 5 )³

= 10³ ( perfect cube )

$Now , Cube \:root \:of \:1000$

$= \sqrt[3] {1000}$

$= \sqrt[3]{(10^{3}) }$

$= 10$

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Answer 2

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