Question

4 root 3 + root 2 minus 2 upon root 5 minus root 3 minus 3 upon root 2 minus root 5 simplified

Answer 1

$$\begin{gathered} 4\sqrt{3}+\sqrt{2}-\frac{2}{\sqrt{5}-\sqrt{3}}-\frac{3}{\sqrt{2}-\sqrt{5}} \\ =4\sqrt{3}+\sqrt{2}-\frac{2}{\sqrt{5}-\sqrt{3}}\times \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}+\sqrt{3}}-\frac{3}{\sqrt{2}-\sqrt{5}}\times \frac{\sqrt{2}+\sqrt{5}}{\sqrt{2}+\sqrt{5}} \\ =4\sqrt{3}+\sqrt{2}-\frac{2\left(\sqrt{5}+\sqrt{3}\right)}{5-3}-\frac{3\left(\sqrt{2}+\sqrt{5}\right)}{2-5} \\ =4\sqrt{3}+\sqrt{2}-\sqrt{5}-\sqrt{3}+\sqrt{2}+\sqrt{5} \\ =3\sqrt{3}+2\sqrt{2} \end{gathered}$$