Question

Find the smallest number by which 3645 must be divided so that it becomes a
perfect square. Also, find the square root of the resulting number.​

Answer 1

${ \large{ \sf{ \underbrace{\underline{\bigstar \:We \:have \:to \:find \::-}}}}}$

$\textit\color{red}{1.}$

$\sf\color{violet}{Smallest\: number \:by\: which\: 3645 \:must\: be \:divided \:so \:that \:it \:becomes\: a\: perfect \:square.}$

$\textit\color{red}{2.}$

$\sf\color{violet}{Find\: the \:square \:root \:of\: the \:resulting\: number.}$

${ \large{ \sf{ \underbrace{\underline{\bigstar \:Given\: that,}}}}}$

$\bold\color{green}{3645}$$\sf\color{red}{= (3 × 3) × (3 × 3) × 5 × 3}$

$\sf\color{red}{=32 × 32 × 5 × 3}$

To make the unpaired$\tt\color{violet}{5}$ and $\tt\color{violet}{3}$ into paired, the number$\tt\color{violet}{3645}$ has to be divided by

$\sf\color{magenta}{5 × 3=15 3645 ÷ 15}$

$\sf\color{magenta}{= 32 × 32}$

$\textbf\color{gold}{Square\: root}$

$\sf\color{darkgreen}{√(3645 ÷ 15)}$

$\textit\color{brown}{= 3 × 3}$

$\sf\bold\color{darkblue}{ = 9}$

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Thankyou :)

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