Question

by which smallest number should 42592 be divided so that the quotient is a perfect cube?

Answer 1

this is your answer

Answer 2

Answer:

4 is the smallest number should 42592 be divided so that the quotient is a perfect cube.

Step-by-step explanation:

To find : By which smallest number should 42592 be divided so that the quotient is a perfect cube?

Solution :

We factories the number,

$42592=2\times2\times2\times2\times2\times11\times 11 \times11$

$42592=2^3\times11^3\times4$

To make the number a perfect cube we have to divide the number by 4,

As $\frac{42592}{4}=\frac{2^3\times11^3\times4}{4}=2^3\times 11^3$

$10648=(2\times 11)^3$

$10648=22^3$

Therefore, 4 is the smallest number should 42592 be divided so that the quotient is a perfect cube.