How do you simplify sqrt(2/3)*sqrt(6/5)?

Jun 9, 2018

$\frac{6 \sqrt{5}}{15}$

Explanation:

Use the rule for radicals of the same degree:

$\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$

$\sqrt{\frac{2}{3}} \cdot \sqrt{\frac{6}{5}} = \sqrt{\frac{2}{3} \cdot \frac{6}{5}} = \sqrt{\frac{12}{15}}$

now use the rule for radicals of the same degree:

$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$

$\sqrt{\frac{12}{15}} = \frac{\sqrt{12}}{\sqrt{15}}$

now rationalize the denominator:

$\frac{\sqrt{12}}{\sqrt{15}} \cdot \frac{\sqrt{15}}{\sqrt{15}} = \frac{\sqrt{180}}{15} = \frac{6 \sqrt{5}}{15}$

Jun 9, 2018

$\frac{2 \cdot \sqrt{5}}{5}$
$\sqrt{a} \cdot \sqrt{b} = \sqrt{a b}$ for $a , b \ge 0$
$\sqrt{\frac{2}{3}} \cdot \sqrt{\frac{6}{5}} = \sqrt{\frac{4}{5}} = \frac{2}{\sqrt{5}} = \frac{2 \cdot \sqrt{5}}{5}$