# Chapter 10 - Section 10.4 - Adding, Subtracting, and Multiplying Radical Expressions - Exercise Set: 49

$(\sqrt{5}-\sqrt{2})^{2}=7-2\sqrt{10}$

#### 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: $(\sqrt{5}-\sqrt{2})^{2}=(\sqrt{5})^{2}-2(\sqrt{5})(\sqrt{2})+(\sqrt{2})^{2}=...$ $...=5-2\sqrt{10}+2=7-2\sqrt{10}$

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