Question

simplify.
\sqrt{\frac{6}{15}}

Explanation:

Step1: Simplify the fraction inside the square root

First, we simplify the fraction \(\frac{6}{15}\). Both the numerator and the denominator are divisible by 3. So, \(\frac{6\div3}{15\div3}=\frac{2}{5}\). Now our expression becomes \(\sqrt{\frac{2}{5}}\).

Step2: Rationalize the denominator

To rationalize the denominator, we multiply the numerator and the denominator inside the square root by \(\sqrt{5}\) (since the denominator is \(\sqrt{5}\) when we consider \(\sqrt{\frac{2}{5}}=\frac{\sqrt{2}}{\sqrt{5}}\)). So we have:

$$ \sqrt{\frac{2\times5}{5\times5}}=\sqrt{\frac{10}{25}} $$

Step3: Simplify the square root

Since \(\sqrt{\frac{10}{25}}=\frac{\sqrt{10}}{\sqrt{25}}\) and \(\sqrt{25} = 5\), we get \(\frac{\sqrt{10}}{5}\).

Answer:

\(\frac{\sqrt{10}}{5}\)