Question

What is the smallest number by which 8788 must be divided to obtain a perfect cube?

Answer 1

$\:\: \underline{\underline{\bf{\large\mathfrak{~~Solution~~}}}}$

the cube root of 8788 is

$= \sqrt[3]{8788} \\ = \sqrt[3]{13 \times 13 \times 13 \times 2 \times 2} \\ = 13 \sqrt[3]{2 \times 2}$

so 8788 should be multiplied by 2 to be a perfect cube......

so 8788 should be divided by 4 to be a perfect cube......

$\:\: \underline{\underline{\bf{\large\mathfrak{~hope ~this ~help~you~~}}}}$

Answer 2

$\huge{\mathfrak{\green{S}}}{\mathfrak{o}}{\mathfrak {\orange {l}}}{\mathfrak{\red{u}}}{\mathfrak {\pink {t}}}{\mathfrak{\blue{i}}}{\mathfrak{\purple {o}}}{\mathfrak {\gray {n}}}$

$\sf= > 8788 = 2×2×13×13×13 \\ </h3><h3>\sf = > 8788 =2 {}^{2} ×13 {}^{3} \\ </h3><h3>\sf = > 8788 = 4×13 {}^{3} \\ </h3><h3>\sf = > \frac{8788}{4} = 13 {}^{3}$

Hence ,while dividing 8788 with a smallest number and we get quotient is a perfect cube is 4