Question

Which of the following is the correct simplified form of $\frac{5}{\sqrt{9}-\sqrt{8}}$ ?

• A. $15+10\sqrt{2}$
• B. $10\sqrt{5}$
• C. $3+2\sqrt{2}$
• D. None of the above

Answer 1

The correct option is A $15+10\sqrt{2}$

First, we need to rationalise the denominator of $\frac{5}{\sqrt{9}-\sqrt{8}}$

$\Rightarrow \frac{5}{\sqrt{9}-\sqrt{8}}=\frac{5}{\sqrt{9}-\sqrt{8}}\times \frac{\sqrt{9}+\sqrt{8}}{\sqrt{9}+\sqrt{8}}\Rightarrow \frac{5}{\sqrt{9}-\sqrt{8}}=\frac{5(\sqrt{9}+\sqrt{8})}{9-8}\Rightarrow \frac{5}{\sqrt{9}-\sqrt{8}}=5(3+2\sqrt{2})\Rightarrow \frac{5}{\sqrt{9}-\sqrt{8}}=15+10\sqrt{2}$