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NCERT Exemplar Solutions Class 9 Mathematics Solutions for Number Systems - Exercise 1.1 in Chapter 1 - Number Systems
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\frac{1}{\sqrt{9}-\sqrt{8}} is equal to ________.
Answer:
\begin{aligned} & \frac{1}{\sqrt{9}-\sqrt{8}}=\frac{1}{\sqrt{3 \times 3}-\sqrt{4 \times 2}}=\frac{1}{3-2 \sqrt{2}}\\ &=\frac{1}{3-2 \sqrt{2}} \times \frac{3+2 \sqrt{2}}{3+2 \sqrt{2}}=\frac{3+2 \sqrt{2}}{(3)^{2}-(2 \sqrt{2})^{2}}\\ &=\frac{3+2 \sqrt{2}}{9-8}=\frac{3+2 \sqrt{2}}{1}=3+2 \sqrt{2} \end{aligned}
Hence, (D) is the correct answer.
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