Question

By which smallest number must 5400 be multiplied to make it a perfect cube?​

Answer 1

$\leadsto\sf\purple{Solution:-}$

$\sf{First \: do \: prime \: factorisation \: of \: } \sf \purple{5400}$

$\begin{array}{r | l}2 &5400\\ 2&2700\\2&1350\\ 3&675\\ 3&225 \\ 3&75\\ 5&25\\ 5&5\\&1 \end{array}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\sf{\sqrt[3]{5400} = \sqrt[3]{2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 5 \times 5}}$

$\sf\purple{Now \: make \: triplet \: means \: group \: of \: 3 \: numbers}$

$\sf{\sqrt[3]{5400} = 2 \times 3 \times \sqrt[2]{5} }$

$\sf \purple{ 5 \: is \: not \: in \: a \: triplet \: group \: so \: 5400 \: is \: not \: a \: perfect \: cube}$

$\sf{5 \: is \: the \: smallest \: number \: which \: must \: be \: multiplied \: in \: 5400 \: to \: make \: it \: a \: perfect \: cube}$