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$\newcommand{\amp}{&}$

Simplify $\sqrt{125}\text{.}$

To type $\sqrt{\phantom{x}}\text{,}$ use sqrt( ).

Solution

Here is a table of factor pairs for the number $125\text{.}$

$\begin{aligned} 1\amp\cdot125\\ 5\amp\cdot25 \end{aligned}$

The largest perfect square is $25$ so we will rewrite $125$ as $25\cdot5\text{.}$

$\begin{aligned} \sqrt{125}\amp=\sqrt{25\cdot5}\\ \amp=\sqrt{25}\cdot\sqrt{5}\\ \amp=5\sqrt{5} \end{aligned}$