Question

What is the value of $(\frac{1}{\sqrt{9}-\sqrt{8}}-\frac{1}{\sqrt{8}-\sqrt{7}}+\frac{1}{\sqrt{7}-\sqrt{6}}-\frac{1}{\sqrt{6}-\sqrt{5}}+\frac{1}{\sqrt{5}-\sqrt{4}})$

• A. $0$
• B. $\frac{1}{3}$
• C. $1$
• D. $5$

Answer 1

The correct option is D $5$

$\frac{1}{\sqrt{9}-\sqrt{8}}-\frac{1}{\sqrt{8}-\sqrt{7}}+\frac{1}{\sqrt{7}-\sqrt{6}}-\frac{1}{\sqrt{6}-\sqrt{5}}+\frac{1}{\sqrt{5}-\sqrt{4}}$

rationalisation

$\frac{\sqrt{9}+\sqrt{8}}{1}-\frac{-(\sqrt{8}+\sqrt{7})}{1}+\frac{(\sqrt{7}+\sqrt{6})}{1}-\frac{-(\sqrt{6}+\sqrt{5})}{1}+\frac{(\sqrt{5}+\sqrt{1})}{1}$

$\Rightarrow \sqrt{9}+\sqrt{8}-\sqrt{8}-\sqrt{7}+\sqrt{7}+\sqrt{6}-\sqrt{6}-\sqrt{5}+\sqrt{5}+\sqrt{4}$

$=3+2=5$