Dear Sir ,
I felt difficulty in solving the following problems .So please help me to solve these questions . I will be very thankful to you .\
The question is in the attachment .
Hello, rsaravanan!
Here is the first one . . .
$\displaystyle \text{1) If }\,a \:=\:7-4\sqrt{3},\;\text{ find: }\,\sqrt{a} + \frac{1}{\sqrt{a}}$
$\displaystyle \text{Note that: }\:a \;=\;7 - 4\sqrt{3} \;=\; (2-\sqrt{3})^2$
$\displaystyle \text{Hence: }\:\sqrt{a} \;=\;\sqrt{(2-\sqrt{3})^2} \;=\;2-\sqrt{3}$
$\displaystyle \text{Then: }\:\sqrt{a} + \frac{1}{\sqrt{a}} \;=\;\left(2-\sqrt{3}\right) + \frac{1}{2-\sqrt{3}}$
$\displaystyle \text{Rationalize: }\:\left(2-\sqrt{3}\right)\;+\; \frac{1}{2-\sqrt{3}}\!\cdot\!{\color{blue}\frac{2+\sqrt{3}}{2 +\sqrt{3}}} \;\;=\;\;\left(2-\sqrt{3}\right)\;+\;\frac{2+\sqrt{3}}{4-3} $
. . . . . . . . . . $\displaystyle =\;\;\left(2 - \sqrt{3}\right) + \left(2 + \sqrt{3}\right) \;\;=\;\;\boxed{4}$