Question

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

Explanation:

Step1: Simplify the denominator

First, simplify $\sqrt{8}=\sqrt{4\times2}=2\sqrt{2}$. So the fraction becomes $\frac{1}{2\sqrt{2}}$.

Step2: Rationalize the denominator

Multiply the numerator and denominator by $\sqrt{2}$. We get $\frac{1\times\sqrt{2}}{2\sqrt{2}\times\sqrt{2}}$.

Step3: Calculate the new - fraction

Since $\sqrt{2}\times\sqrt{2} = 2$, the fraction is $\frac{\sqrt{2}}{2\times2}=\frac{\sqrt{2}}{4}$.

Answer:

$\frac{\sqrt{2}}{4}$