Question

question
express in simplest form with a rational denominator.
\\(\frac{4}{\sqrt{20}}\\)
answer attempt 1 out of 20
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Explanation:

Step1: Simplify the square root in the denominator

We know that $\sqrt{20}=\sqrt{4\times5}$. By the property of square roots $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ (where $a = 4$ and $b=5$ and $a\geq0,b\geq0$), we have $\sqrt{4\times5}=\sqrt{4}\times\sqrt{5}=2\sqrt{5}$. So the expression becomes $\frac{4}{2\sqrt{5}}$.

Step2: Simplify the fraction

We can simplify $\frac{4}{2\sqrt{5}}$ by dividing the numerator and the denominator by 2. So $\frac{4\div2}{2\sqrt{5}\div2}=\frac{2}{\sqrt{5}}$.

Step3: Rationalize the denominator

To rationalize the denominator of $\frac{2}{\sqrt{5}}$, we multiply the numerator and the denominator by $\sqrt{5}$. So we get $\frac{2\times\sqrt{5}}{\sqrt{5}\times\sqrt{5}}$. Since $\sqrt{5}\times\sqrt{5}=5$, the expression is $\frac{2\sqrt{5}}{5}$.

Answer:

$\frac{2\sqrt{5}}{5}$