# What is (square root of 3) to the power of 2?

Sep 9, 2015

${\left(\sqrt{3}\right)}^{2} = 3$

#### Explanation:

Some Rules Concerning Exponents That Are Relevant To This Question:

$\textcolor{w h i t e}{\text{XXX}} {\left({b}^{m}\right)}^{n} = {b}^{m x}$

$\textcolor{w h i t e}{\text{XXX}} \sqrt{b} = {b}^{\frac{1}{2}}$

Therefore $\sqrt{3} = {3}^{\frac{1}{2}}$
and
${\left(\sqrt{3}\right)}^{2} = {\left({3}^{\frac{1}{2}}\right)}^{2} = {3}^{\frac{1}{2} \times 2} = {3}^{1} = 3$