Question

7 root 3 / root 10+ root 3-2 root 3/ root 6+ root 5-3 root 2/ root 15+ 3 root 2

Answer 1

$$\begin{gathered} \frac{7\sqrt{3}}{\sqrt{10}+\sqrt{3}}-\frac{2\sqrt{3}}{\sqrt{6}+\sqrt{5}}-\frac{3\sqrt{2}}{\sqrt{15}+3\sqrt{2}} \\ =\left[\frac{7\sqrt{3}}{\sqrt{10}+\sqrt{3}}\times \frac{\left(\sqrt{10}-\sqrt{3}\right)}{\left(\sqrt{10}-\sqrt{3}\right)}\right]-\left(\frac{2\sqrt{3}}{\sqrt{6}+\sqrt{5}}\times \frac{\sqrt{6}-\sqrt{5}}{\sqrt{6}-\sqrt{5}}\right)-\left(\frac{3\sqrt{2}}{\sqrt{15}+3\sqrt{2}}\times \frac{\sqrt{15}-3\sqrt{2}}{\sqrt{15}-3\sqrt{2}}\right) \\ =\left(\frac{7\sqrt{30}-21}{10-3}\right)-\left(\frac{6\sqrt{2}-2\sqrt{15}}{6-5}\right)-\left(\frac{3\sqrt{30}-18}{15-18}\right) \\ =\sqrt{30}-3-6\sqrt{2}+2\sqrt{15}+\sqrt{30}-6 \\ =2\sqrt{30}+2\sqrt{15}-6\sqrt{2}-9 \end{gathered}$$