Question

simplify.
\sqrt{\frac{2}{3}}

Explanation:

Step1: Rationalize the denominator

To simplify $\sqrt{\frac{2}{3}}$, we multiply the numerator and denominator inside the square root by 3 to rationalize the denominator. So we have $\sqrt{\frac{2\times3}{3\times3}}$.

Step2: Simplify the square root

Simplify the expression inside the square root: $\sqrt{\frac{6}{9}}$. Since $\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$ (for $a\geq0,b > 0$), we can write this as $\frac{\sqrt{6}}{\sqrt{9}}$. And $\sqrt{9} = 3$, so the simplified form is $\frac{\sqrt{6}}{3}$.

Answer:

$\frac{\sqrt{6}}{3}$