How do you simplify sqrt 50 - sqrt 98?

Jul 8, 2016

$\sqrt{50} - \sqrt{98} = \textcolor{b l u e}{- 2 \sqrt{2}}$
$\textcolor{red}{\sqrt{50}} = \sqrt{{5}^{2} \cdot 2} = \sqrt{{5}^{2}} \cdot \sqrt{2} = \textcolor{red}{5 \sqrt{2}}$
$\textcolor{g r e e n}{\sqrt{98}} = \sqrt{{7}^{2} \cdot 2} = \sqrt{{7}^{2}} \cdot \sqrt{2} = \textcolor{g r e e n}{7 \sqrt{2}}$
$\textcolor{red}{\sqrt{50}} - \textcolor{g r e e n}{\sqrt{98}} = \textcolor{red}{5 \sqrt{2}} - \textcolor{g r e e n}{7 \sqrt{2}} = \left(5 - 7\right) \sqrt{2} = \textcolor{b l u e}{- 2 \sqrt{2}}$