How do you simplify sqrt(2/3)*sqrt(3/7)?

Aug 23, 2017

See a solution process below:

Explanation:

We can use this rule for multiplying radicals:

$\sqrt{\textcolor{red}{a}} \cdot \sqrt{\textcolor{b l u e}{b}} = \sqrt{\textcolor{red}{a} \cdot \textcolor{b l u e}{b}}$

$\sqrt{\textcolor{red}{\frac{2}{3}}} \cdot \sqrt{\textcolor{b l u e}{\frac{3}{7}}} \implies \sqrt{\textcolor{red}{\frac{2}{3}} \cdot \textcolor{b l u e}{\frac{3}{7}}} \implies \sqrt{\textcolor{red}{\frac{2}{\textcolor{b l a c k}{\cancel{\textcolor{red}{3}}}}} \cdot \textcolor{b l u e}{\frac{\textcolor{b l a c k}{\cancel{\textcolor{b l u e}{3}}}}{7}}} \implies$

$\sqrt{\frac{2}{7}}$

If necessary we can rationalize the denominator. Or in other words, remove the radical from the denominator:

We can rewrite the radical as:

$\frac{\sqrt{2}}{\sqrt{7}} \implies \frac{\sqrt{7}}{\sqrt{7}} \times \frac{\sqrt{2}}{\sqrt{7}} \implies \frac{\sqrt{7} \times \sqrt{2}}{\sqrt{7}} ^ 2 \implies \frac{\sqrt{7 \times 2}}{7} \implies$

$\frac{\sqrt{14}}{7}$