Question

kindly answer
56. $\sqrt{2-\sqrt{3}}$ can be expressed as
$$\begin{gathered} \text{(1) 2 -}\frac{1}{\sqrt{3}} \\ \text{(2) 3 -}\frac{1}{\sqrt{2}} \\ \text{(3)}\frac{1+\sqrt{3}}{\sqrt{2}} \\ \text{(4)}\frac{\sqrt{3}\text{- 1}}{\sqrt{2}} \end{gathered}$$

Answer 1

$$\begin{gathered} \sqrt{2-\sqrt{3}} \\ =\sqrt{\frac{2\left(2-\sqrt{3}\right)}{2}} \\ =\sqrt{\frac{4-2\sqrt{3}}{2}} \\ =\sqrt{\frac{3+1-2\sqrt{3}}{2}} \\ =\sqrt{\frac{{\left(\sqrt{3}\right)}^2+{\left(1\right)}^2-2\left(\sqrt{3}\right)\left(1\right)}{2}} \\ =\sqrt{\frac{{\left(\sqrt{3}-1\right)}^2}{2}} \\ =\frac{\sqrt{3}-1}{\sqrt{2}} \end{gathered}$$