Question

$$A=\frac{3}{\sqrt{5+\sqrt{2}}+\frac{1}{\sqrt{3}-\sqrt{2}}-\frac{2}{\sqrt{5}+\sqrt{3}}$$

Answer

A=sqrt(5)+2*sqrt(3)

Solution


Simplify  \(1\times \sqrt{3}\)  to  \(\sqrt{3}\).
\[A=3\sqrt{5}+\sqrt{2}+\sqrt{3}-\sqrt{2}-2\sqrt{5}+\sqrt{3}\]
Simplify  \(3\sqrt{5}+\sqrt{2}+\sqrt{3}-\sqrt{2}-2\sqrt{5}+\sqrt{3}\)  to  \(\sqrt{5}+2\sqrt{3}\).
\[A=\sqrt{5}+2\sqrt{3}\]

Decimal Form: 5.700170