Question

Value of the below expresssion is

$\frac{1}{\sqrt[2]{26}+\sqrt[2]{25}}$ + $\frac{1}{\sqrt[2]{27}+\sqrt[2]{26}}$ + $\frac{1}{\sqrt[2]{28}+\sqrt[2]{27}}$

• A. $\sqrt[2]{26}+\sqrt[2]{27}$
• B. $\sqrt[2]{28}+\sqrt[2]{25}$
• C. $\sqrt[2]{28}-\sqrt[2]{25}$
• D. $\sqrt[2]{25}-\sqrt[2]{28}$

Answer 1

The correct option is C

$\sqrt[2]{28}-\sqrt[2]{25}$

Given expression is

$\frac{1}{\sqrt[2]{26}+\sqrt[2]{25}}$ + $\frac{1}{\sqrt[2]{27}+\sqrt[2]{26}}$ + $\frac{1}{\sqrt[2]{28}+\sqrt[2]{27}}$

= $\frac{}{\sqrt[2]{26}+\sqrt[2]{25}}$ $\times$ $\frac{\sqrt[2]{26}-\sqrt[2]{25}}{\sqrt[2]{26}-\sqrt[2]{25}}$ + $\frac{}{\sqrt[2]{27}+\sqrt[2]{26}}$ $\times$ $\frac{\sqrt[2]{27}-\sqrt[2]{26}}{\sqrt[2]{27}-\sqrt[2]{26}}$ + $\frac{}{\sqrt[2]{28}+\sqrt[2]{27}}$ $\times$ $\frac{\sqrt[2]{28}-\sqrt[2]{27}}{\sqrt[2]{28}-\sqrt[2]{27}}$

= $\frac{\sqrt[2]{26}-\sqrt[2]{25}}{(\sqrt[2]{26}{)}^2-(\sqrt[2]{25}{)}^2}$ + $\frac{\sqrt[2]{27}-\sqrt[2]{26}}{(\sqrt[2]{27}{)}^2-(\sqrt[2]{26}{)}^2}$ + $\frac{\sqrt[2]{28}-\sqrt[2]{27}}{(\sqrt[2]{28}{)}^2-(\sqrt[2]{27}{)}^2}$

= $\frac{\sqrt[2]{26}-\sqrt[2]{25}}{6-5}$ + $\frac{\sqrt[2]{27}-\sqrt[2]{26}}{7-6}$ + $\frac{\sqrt[2]{28}-\sqrt[2]{27}}{8-7}$

= $\sqrt[2]{26}-\sqrt[2]{25}$ + $\sqrt[2]{27}-\sqrt[2]{26}$ + $\sqrt[2]{28}-\sqrt[2]{27}$

= $\sqrt[2]{28}-\sqrt[2]{25}$