If x = 5 - 2√6, then what is the value of √x +(1/√x)?

Given : x = 5 - 2√6

=> $$x=3+2-2\sqrt{(3)(2)}$$

=> $$x=(\sqrt3)^2+(\sqrt2)^2-2(\sqrt3)(\sqrt2)$$

=> $$x=(\sqrt3-\sqrt2)^2$$

=> $$\sqrt{x}=\sqrt3-\sqrt2$$ -----------(i)

=> $$\frac{1}{\sqrt{x}}=\frac{1}{\sqrt3-\sqrt2}$$

=> $$\frac{1}{\sqrt{x}}=\frac{1}{\sqrt3-\sqrt2}\times\frac{(\sqrt3+\sqrt2)}{(\sqrt3+\sqrt2)}$$

=> $$\frac{1}{\sqrt{x}}=\frac{\sqrt3+\sqrt2}{3-2}=\sqrt3+\sqrt2$$ -------------(ii)

To find : $$\sqrt{x}+\frac{1}{\sqrt{x}}$$

Using equations (i) and (ii), we get :

= $$(\sqrt3-\sqrt2)+(\sqrt3+\sqrt2)$$

= $$2\sqrt3$$

=> Ans - (C)