MCQ
Write the correct answer in the following: $\frac{1}{\sqrt{9}-\sqrt{8}}$ is equal to
- A$\frac{1}{2}(3-2\sqrt{2})$
- B$\frac{1}{3+2\sqrt{2}}$
- C$3-2\sqrt{2}$
- ✓$3+2\sqrt{2}$
✓
Answer
Correct option: D.
$3+2\sqrt{2}$
$\frac{1}{\sqrt{9}-\sqrt{8}}=\frac{1}{3-2\sqrt{2}}=\frac{1}{3-2\sqrt{2}}\cdot\frac{3+2\sqrt{2}}{3+2\sqrt{2}}$ $[\because\sqrt{8}=\sqrt{2\times2\times2}=2\sqrt{2}]$
$[$multiplying numerator and denominator by $3+2\sqrt{2}]$
$\frac{3+2\sqrt{2}}{9-(2-\sqrt{2})^2}$$[\text{using identity (a}-\text{b})(\text{a+b})=\text{a}^2-\text{b}^2]$
$=\frac{3+2\sqrt{2}}{9-8}=3+2\sqrt{2}$
$[$multiplying numerator and denominator by $3+2\sqrt{2}]$
$\frac{3+2\sqrt{2}}{9-(2-\sqrt{2})^2}$$[\text{using identity (a}-\text{b})(\text{a+b})=\text{a}^2-\text{b}^2]$
$=\frac{3+2\sqrt{2}}{9-8}=3+2\sqrt{2}$
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