Question

express in simplest form with a rational denominator.
\\(\frac{1}{\sqrt{20}}\\)

Explanation:

Step1: Simplify the square root

First, we simplify $\sqrt{20}$. We know that $20 = 4\times5$, and $\sqrt{4\times5}=\sqrt{4}\times\sqrt{5}=2\sqrt{5}$. So, $\frac{1}{\sqrt{20}}=\frac{1}{2\sqrt{5}}$.

Step2: Rationalize the denominator

To rationalize the denominator, we multiply the numerator and the denominator by $\sqrt{5}$. So, $\frac{1\times\sqrt{5}}{2\sqrt{5}\times\sqrt{5}}=\frac{\sqrt{5}}{2\times5}=\frac{\sqrt{5}}{10}$.

Answer:

$\frac{\sqrt{5}}{10}$