Question

The value of $\frac{1}{\sqrt{10}-\sqrt{9}}-\frac{1}{\sqrt{11}-\sqrt{10}}+\frac{1}{\sqrt{12}-\sqrt{11}}$ $-....-\frac{1}{\sqrt{121}-\sqrt{120}}$ is equal to

• A. $-10$
• B. 11
• C. 14
• D. 13
• E. $-8$

Answer 1

Answer: (E)

We have $\frac{1}{\sqrt{10}-\sqrt{9}}-\frac{1}{\sqrt{11}-\sqrt{10}}+\frac{1}{\sqrt{12}-\sqrt{11}}$ $-....-\frac{1}{\sqrt{121}-\sqrt{120}}$
$=\sqrt{10}+\sqrt{9}-\sqrt{11}-\sqrt{10}+\sqrt{12}+\sqrt{11}$ $-.....-\sqrt{121}-\sqrt{120}$
$=\sqrt{9}-\sqrt{121}=3-11=-8$