# How do you find a perfect square and simplify sqrt(50)?

Apr 8, 2015

Factor $50$ and look for terms that show up an even number of times (a pair of such terms form a perfect square)>

$50$
$= 2 \times 25$
$= 2 \times 5 \times 5$
no further factorization is possible

$5 \times 5$ form a perfect square ($25$)

$\sqrt{50}$ can be written as $\sqrt{25} \cdot \sqrt{2}$
$= 5 \sqrt{2}$