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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

5-2\sqrt{6}

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}

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