# How do you rewrite with rational exponents: sqrt2?

$\sqrt{2} = {2}^{\frac{1}{2}}$
Note that if $x > 0$ then ${x}^{a} {x}^{b} = {x}^{a + b}$
So we find ${\left({2}^{\frac{1}{2}}\right)}^{2} = {2}^{\frac{1}{2}} \cdot {2}^{\frac{1}{2}} = {2}^{\frac{1}{2} + \frac{1}{2}} = {2}^{1} = 2$
So ${2}^{\frac{1}{2}}$ is a square root of $2$ since if you square it you get $2$.