Question

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

• A. 0
• B. 1
• C. 5
• D. 3

Answer 1

The correct option is C

5

Rationalize the terms, we get
$\frac{1}{\sqrt{9}-\sqrt{8}}\times \frac{\sqrt{9}+\sqrt{8}}{\sqrt{9}+\sqrt{8}}=\frac{\sqrt{9}+\sqrt{8}}{1}\frac{1}{\sqrt{8}-\sqrt{7}}\times \frac{\sqrt{8}+\sqrt{7}}{\sqrt{8}+\sqrt{7}}=\frac{\sqrt{8}+\sqrt{7}}{1}\frac{1}{\sqrt{7}-\sqrt{6}}\times \frac{\sqrt{7}+\sqrt{6}}{\sqrt{7}+\sqrt{6}}=\frac{\sqrt{7}+\sqrt{6}}{1}\frac{1}{\sqrt{6}-\sqrt{5}}\times \frac{\sqrt{6}+\sqrt{5}}{\sqrt{6}+\sqrt{5}}=\frac{\sqrt{6}+\sqrt{5}}{1}\frac{1}{\sqrt{5}-\sqrt{4}}\times \frac{\sqrt{5}+\sqrt{4}}{\sqrt{5}+\sqrt{4}}=\frac{\sqrt{5}+\sqrt{4}}{1}$
So, we get $(\sqrt{9}+\sqrt{8})-(\sqrt{8}+\sqrt{7})+(\sqrt{7}+\sqrt{6})-(\sqrt{6}+\sqrt{5})+(\sqrt{5}+\sqrt{4})=3+2=5$