Question

The expression $\frac{(5\sqrt{3}+\sqrt{50})(5-\sqrt{24})}{\sqrt{75}-5\sqrt{2}}$ simplifies to

• A. 1
• B. $\sqrt{3}-\sqrt{2}$
• C. $\sqrt{6}-\sqrt{5}$
• D. $\sqrt{2}$

Answer 1

The correct option is A 1

$\frac{(5\sqrt{3}+\sqrt{50})(5-\sqrt{24})}{\sqrt{75}-5\sqrt{2}}$
$\Rightarrow \frac{(5\sqrt{3}+5\sqrt{2})(5-2\sqrt{6})}{5\sqrt{3}-5\sqrt{2}}$
$\Rightarrow \frac{25\sqrt{3}+25\sqrt{2}-10\sqrt{18}-10\sqrt{12}}{5\sqrt{3}-5\sqrt{2}}$
$\Rightarrow \frac{25\sqrt{3}+25\sqrt{2}-30\sqrt{2}-20\sqrt{3}}{5\sqrt{3}-5\sqrt{2}}$
$\Rightarrow \frac{5\sqrt{3}-5\sqrt{2}}{5\sqrt{3}-5\sqrt{2}}$
$\Rightarrow \frac{5(\sqrt{3}-\sqrt{2})}{5(\sqrt{3}-\sqrt{2})}=1$