How do you simplify square root 125 + square root 1/5 - square root 49/5?

Oct 7, 2015

$\sqrt{125} + \sqrt{\frac{1}{5}} - \sqrt{\frac{49}{5}} = \frac{19}{\sqrt{5}}$

Explanation:

$\sqrt{125} = \sqrt{25 \cdot 5} = \sqrt{25 \cdot \frac{25}{5}} = \sqrt{{25}^{2} / 5} = \frac{\sqrt{{25}^{2}}}{\sqrt{5}} = \frac{25}{\sqrt{5}}$

$\sqrt{\frac{1}{5}} = \frac{\sqrt{1}}{\sqrt{5}} = \frac{1}{\sqrt{5}}$

$\sqrt{\frac{49}{5}} = \sqrt{{7}^{2} / 5} = \frac{\sqrt{{7}^{2}}}{\sqrt{5}} = \frac{7}{\sqrt{5}}$

$\rightarrow \sqrt{125} + \sqrt{\frac{1}{5}} - \sqrt{\frac{49}{5}} = \frac{25}{\sqrt{5}} + \frac{1}{\sqrt{5}} - \frac{7}{\sqrt{5}} = \frac{25 + 1 - 7}{\sqrt{5}} = \frac{19}{\sqrt{5}}$