Question

IF $x=7+4\sqrt{3},$ then the value of $\sqrt{x}+\frac{1}{\sqrt{x}}$ is

• A. $8$
• B. $6$
• C. $5$
• D. $4$

Answer 1

The correct option is D $4$

Given that:

$x=7+4\sqrt{3}$

So,

$\Rightarrow (\sqrt{x}+\frac{1}{\sqrt{x}}{)}^2$

$\Rightarrow x+2+\frac{1}{x}$

$\Rightarrow 7+4\sqrt{3}+2+\frac{1}{7+4\sqrt{3}}$

$\Rightarrow 9+4\sqrt{3}+\frac{1}{7+4\sqrt{3}}\times \frac{7-4\sqrt{3}}{7-4\sqrt{3}}$

$\Rightarrow 16$

Hence,

$\Rightarrow (\sqrt{x}+\frac{1}{\sqrt{x}})=4.$