Question

find the smallest number by which 8788be divided so that the quptient is a perfect cube. ​

Answer 1

$\huge{\mathfrak{\underline{\underline{Solution:-}}}}$

$\mathtt{The\: given\:number\:is\:8788.}$

$\mathtt{The\: prime\: factorization\:of\:8788\:is\: given\:by,}$

$\mathtt{8788=2×2×13×13×13}$

We see that prime factor of 2 does not occur in the group of 3, hence the given number is not a perfect cube.

We see that prime factor of 2 does not occur in the group of 3, hence the given number is not a perfect cube.In order to make it perfect cube, it must be divided by 4.

Now,

$\mathtt{\frac{8788}{4}=\frac{2×2×13×13×13}{4}}$

$\mathtt{\implies 2197= 13×13×13,}$

$\mathtt{Which\:is\: perfect\:cube\:number.}$

$\mathtt{\sqrt[3]{2197} = \sqrt[3]{13 \times 13 \times 13}=13}$