Question

Simplified form of the expression $\frac{7\sqrt{3}}{\sqrt{10}+\sqrt{3}}-\frac{2\sqrt{5}}{\sqrt{6}+\sqrt{5}}-\frac{3\sqrt{2}}{\sqrt{15}+3\sqrt{2}}$ is?

• A. $1$
• B. $2$
• C. $\frac{1+\sqrt{3}}{5-\sqrt{5}}$
• D. $\frac{2\sqrt{2}}{1+\sqrt{3}}$

Answer 1

The correct option is A $1$

$\frac{7\sqrt{3}}{\sqrt{10}+\sqrt{3}}-\frac{2\sqrt{5}}{\sqrt{6}+\sqrt{5}}-\frac{3\sqrt{2}}{\sqrt{15}+3\sqrt{2}}$

$=\frac{7\sqrt{3}\times (\sqrt{10}-\sqrt{3})}{(\sqrt{10}+\sqrt{3})\times (\sqrt{10}-\sqrt{3})}-\frac{2\sqrt{5}\times (\sqrt{6}-\sqrt{5})}{(\sqrt{6}+\sqrt{5})\times (\sqrt{6}-\sqrt{5})}-\frac{3\sqrt{2}\times (\sqrt{15}-3\sqrt{2})}{(\sqrt{15}+3\sqrt{2})\times (\sqrt{15}-3\sqrt{2})}$

$=\frac{7\sqrt{3}\times (\sqrt{10}-\sqrt{3})}{7}-\frac{2\sqrt{5}\times (\sqrt{6}-\sqrt{5})}{1}-\frac{3\sqrt{2}\times (\sqrt{15}-3\sqrt{2})}{-3}$
$=\sqrt{3}(\sqrt{10}-\sqrt{3})-2\sqrt{5}(\sqrt{6}-\sqrt{5})+\sqrt{2}(\sqrt{15}-3\sqrt{2})$
$=\sqrt{30}-3-2\sqrt{30}+10+\sqrt{30}-6$

$=10-9+2\sqrt{30}-2\sqrt{30}$

$=1$

Hence, option $A.$