Question

express in simplest form with a rational denominator.
\\(\frac{2}{\sqrt{8}}\\)
answer attempt 1 out of 10

Explanation:

Step1: Simplify the square root in the denominator

First, we simplify $\sqrt{8}$. We know that $8 = 4\times2$, and $\sqrt{4\times2}=\sqrt{4}\times\sqrt{2}=2\sqrt{2}$. So the expression becomes $\frac{2}{2\sqrt{2}}$.

Step2: Cancel common factors

We can cancel the common factor of 2 in the numerator and the denominator. So $\frac{2}{2\sqrt{2}}=\frac{1}{\sqrt{2}}$.

Step3: Rationalize the denominator

To rationalize the denominator, we multiply the numerator and the denominator by $\sqrt{2}$. So $\frac{1\times\sqrt{2}}{\sqrt{2}\times\sqrt{2}}=\frac{\sqrt{2}}{2}$.

Answer:

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