# How do you rationalize 10/sqrt8?

May 18, 2018

See a solution process below:

#### Explanation:

To rationalize a fraction you need to multiply the fraction by the appropriate form of $1$ to eliminate the radical in the denominator:

$\frac{\sqrt{8}}{\sqrt{8}} \cdot \frac{10}{\sqrt{8}} \implies \frac{\sqrt{8} \cdot 10}{\sqrt{8} \cdot \sqrt{8}} \implies \frac{10 \sqrt{8}}{8}$

We can simplify this expression as:

$\frac{10 \sqrt{8}}{8} \implies \frac{10 \sqrt{4 \cdot 2}}{8} \implies \frac{10 \sqrt{4} \sqrt{2}}{8} \implies \frac{10 \cdot 2 \sqrt{2}}{8} \implies \frac{20 \sqrt{2}}{8} \implies$

$\frac{4 \cdot 5 \sqrt{2}}{4 \cdot 2} \implies \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} \cdot 5 \sqrt{2}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} \cdot 2} \implies \frac{5 \sqrt{2}}{2}$