express in simplest form with a rational denominator. $\frac{2}{sqrt{8}}$

Explanation:

Step1: Simplify the denominator.

$\sqrt{8}=\sqrt{4\times2}=2\sqrt{2}$ So the fraction becomes $\frac{2}{2\sqrt{2}}$.

Step2: Simplify the fraction.

$\frac{2}{2\sqrt{2}}=\frac{1}{\sqrt{2}}$

Step3: Rationalize the denominator.

Multiply the numerator and denominator by $\sqrt{2}$: $\frac{1\times\sqrt{2}}{\sqrt{2}\times\sqrt{2}}=\frac{\sqrt{2}}{2}$

Answer:

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