Answer
$(\sqrt{5}-\sqrt{2})^{2}=7-2\sqrt{10}$
Work Step by Step
$(\sqrt{5}-\sqrt{2})^{2}$
We can use the formula for squaring a binomial to evaluate this power. The formula is $(a-b)^{2}=a^{2}-2ab+b^{2}$
For this particular case, $a=\sqrt{5}$ and $b=\sqrt{2}$
Substitute the known values into the formula and simplify if possible:
$(\sqrt{5}-\sqrt{2})^{2}=(\sqrt{5})^{2}-2(\sqrt{5})(\sqrt{2})+(\sqrt{2})^{2}=...$
$...=5-2\sqrt{10}+2=7-2\sqrt{10}$
