Powers and Roots – Simplify an expression with roots – Exercise 5673

Exercise

Simplify the expression:

$\frac{\sqrt{3}-\sqrt{2}}{\sqrt{2}+\sqrt{3}}$

Final Answer

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Solution

Using Powers and Roots rules we get:

$\frac{\sqrt{3}-\sqrt{2}}{\sqrt{2}+\sqrt{3}}=$

$=\frac{(\sqrt{3}-\sqrt{2})(\sqrt{2}-\sqrt{3})}{(\sqrt{2}+\sqrt{3})(\sqrt{2}-\sqrt{3})}=$

$=\frac{-{(\sqrt{2}-\sqrt{3})}^2}{2-3}=$

$={(\sqrt{2}-\sqrt{3})}^2=$

$=2-2\cdot\sqrt{2}\sqrt{3}+3=$

$=5-2\sqrt{6}$