How do you add 8sqrt5 - 10sqrt(1/5)?

Apr 20, 2015

$8 \sqrt{5} - 10 \sqrt{\frac{1}{5}} =$

use the property:
for any $A > 0$ it's true that $\sqrt{\frac{1}{A}} = \frac{1}{\sqrt{A}}$ (in our case $A = 5$)
and the fact that a fraction does not change if numerator and denominator are multiplied by the same number (in our case we multiplied them by $\sqrt{5}$)

$= 8 \sqrt{5} - \frac{10}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}} =$

obviously, $\sqrt{5} \cdot \sqrt{5} = 5$ in the denominator
$= 8 \sqrt{5} - 10 \cdot \frac{\sqrt{5}}{5} =$

reduce by $5$ the second item
$= 8 \sqrt{5} - 2 \sqrt{5} = 6 \sqrt{5}$