MCQ
$\frac{1}{\sqrt{9}-\sqrt{8}}$ is equal to:
- A$\frac{1}{3+2\sqrt{2}}$
- B$\frac{1}{2}(3-2\sqrt{2})$
- ✓$3+2\sqrt{2}$
- D$3-2\sqrt{2}$
✓
Answer
Correct option: C.
$3+2\sqrt{2}$
After rationalising
$\frac{1}{\sqrt{9}-\sqrt{8}}=\frac{1}{\sqrt{9}-\sqrt{8}}\times\frac{\sqrt{9}+\sqrt{8}}{\sqrt{9}+\sqrt{8}}$
$=\frac{\sqrt{9}+\sqrt{8}}{(\sqrt{9})^2-(\sqrt{8})^2}$
$=\frac{\sqrt{3\times3}+\sqrt{2\times2\times2}}{9-8}$
$=\frac{3+2\sqrt{2}}{1}$
$=3+2\sqrt{2}$
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