If $$x=7+4\sqrt3$$​, then find the value of $$\sqrt x+\frac{1}{\sqrt x}$$​

Correct option is D

Given: ​

​$$x=7+4\sqrt3$$ 

​$$\sqrt x+\frac{1}{\sqrt x} =?$$ 

Formula Used: ​

​$$(a+b)^2 = a^2 +b^2+2ab$$ 

Solution: ​

​$$x=7+4\sqrt3 \\ \ \\ x = \sqrt 3 +(2)^2+2\times(2)^2\times\sqrt3 \\ \ \\ x=(\sqrt3+2)^2 \\ \ \\ \sqrt x = 2+\sqrt3$$ 

Now, using value of $$\sqrt x$$ 

​$$\sqrt x+\frac{1}{\sqrt x} = 2+\sqrt3 +(2-\sqrt3) \\ \ \\ = 4$$​​