Question

express in simplest form with a rational denominator. \\(\frac{3}{\sqrt{28}}\\)

Explanation:

Step1: Simplify the square root in the denominator

First, we simplify $\sqrt{28}$. We know that $28 = 4\times7$, and $\sqrt{4\times7}=\sqrt{4}\times\sqrt{7}=2\sqrt{7}$. So the expression becomes $\frac{3}{2\sqrt{7}}$.

Step2: Rationalize the denominator

To rationalize the denominator, we multiply the numerator and the denominator by $\sqrt{7}$. So we have $\frac{3\times\sqrt{7}}{2\sqrt{7}\times\sqrt{7}}$.

Step3: Simplify the denominator

Simplify the denominator: $\sqrt{7}\times\sqrt{7} = 7$. So the expression becomes $\frac{3\sqrt{7}}{2\times7}=\frac{3\sqrt{7}}{14}$.

Answer:

$\frac{3\sqrt{7}}{14}$