Question

express in simplest form with a rational denominator. \\(dfrac{3}{sqrt{5}}\\)

Explanation:

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

To rationalize the denominator, we multiply the fraction $\frac{3}{\sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ (since multiplying by 1 doesn't change the value of the fraction). So we have $\frac{3\times\sqrt{5}}{\sqrt{5}\times\sqrt{5}}$.

Step2: Simplify the denominator

We know that $\sqrt{a}\times\sqrt{a}=a$ for $a\geq0$. So $\sqrt{5}\times\sqrt{5} = 5$. The numerator is $3\sqrt{5}$. So the fraction becomes $\frac{3\sqrt{5}}{5}$.

Answer:

$\frac{3\sqrt{5}}{5}$