Find the smallest number by which the given number must be divided to obtain a perfect cube also find the cube root of the quotient: $576$.

Given: A number $576$.

To do: To find the smallest number by which the given number must be divided to obtain a perfect cube and also to find the cube root of the quotient.

Solution:

Given number: $576$

On factorization:

$576=\underline{2\times2\times2}\times\underline{2\times2\times2}\times3\times3$

Therefore, $576$ should be divided by $( 3\times3=9)$ to make it perfect cube.

After dividing $576$ by $9$,

Newly obtained number$=576\div9=64$

Cube root of $64=\sqrt[3]{64}$

$=\sqrt[3]{\underline{2\times2\times2}\times\underline{2\times2\times2}}$

$=2\times2$

$=4$

Thus, $576$ must be divided by $9$ to make it perfect cube, and the quotient is $64$. Cube root of the quotient is $4$.

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Updated on: 10-Oct-2022

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