Question

rationalize the denominator and simplify.
\\(\frac{4}{\sqrt{5}}\\)

Explanation:

Step1: Multiply numerator and denominator by \(\sqrt{5}\)

To rationalize the denominator, we multiply the fraction \(\frac{4}{\sqrt{5}}\) by \(\frac{\sqrt{5}}{\sqrt{5}}\) (since \(\frac{\sqrt{5}}{\sqrt{5}} = 1\), this doesn't change the value of the fraction). So we get \(\frac{4\times\sqrt{5}}{\sqrt{5}\times\sqrt{5}}\).

Step2: Simplify the denominator

We know that \(\sqrt{a}\times\sqrt{a}=a\) for \(a\geq0\). So \(\sqrt{5}\times\sqrt{5} = 5\). Then the fraction becomes \(\frac{4\sqrt{5}}{5}\).

Answer:

\(\frac{4\sqrt{5}}{5}\)