Question

please solve this question

Answer 1

Final Answer : 4

Steps :
1)
$a = 7 - 4 \sqrt{3} \\ = > a = {(2 - \sqrt{3} })^{2} \\ = > \sqrt{a} = 2 - \sqrt{3}$

2)
$\sqrt{a} + \frac{1}{ \sqrt{a} } = 2 - \sqrt{3} + \frac{1}{2 - \sqrt{3} } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 - \sqrt{3} +2 + \sqrt{3} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 4$