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$\newcommand{\multiplyright}[2][\cdot]{{\color{blue}{{{}#1#2}}}}\newcommand{\amp}{&}$

Rationalize the denominator in $\frac{2}{\sqrt{10}}\text{.}$

To type $\sqrt{\phantom{x}}\text{,}$ use sqrt( ).

Solution

We will rationalize the denominator by multiplying the numerator and denominator by $\sqrt{10}\text{:}$

$\begin{aligned} \frac{2}{\sqrt{10}}\amp=\frac{2}{\sqrt{10}}\multiplyright{\frac{\sqrt{10}}{\sqrt{10}}}\\ \amp=\frac{2\cdot\sqrt{10}}{\sqrt{10}\cdot\sqrt{10}}\\ \amp=\frac{2\sqrt{10}}{10}\\ \amp=\frac{\sqrt{10}}{5} \end{aligned}$

Again note that the fraction was simplified in the last step.