Question

rationalize the denominator and simplify.
\sqrt{\frac{2}{6}}

Explanation:

Step1: Simplify the fraction inside the square root

First, simplify \(\frac{2}{6}\) to \(\frac{1}{3}\), so we have \(\sqrt{\frac{1}{3}}\).

Step2: Rationalize the denominator

To rationalize the denominator of \(\sqrt{\frac{1}{3}}\), we multiply the numerator and the denominator inside the square root by \(\sqrt{3}\) (because we want to make the denominator a perfect square). So we get \(\sqrt{\frac{1\times3}{3\times3}}=\sqrt{\frac{3}{9}}\).

Step3: Simplify the square root

Since \(\sqrt{\frac{3}{9}}=\frac{\sqrt{3}}{\sqrt{9}}\) and \(\sqrt{9} = 3\), the simplified form is \(\frac{\sqrt{3}}{3}\).

Answer:

\(\frac{\sqrt{3}}{3}\)