Which of the following options is equal to $$\sqrt{2- \sqrt3}$$​ ?

Correct option is A

Given:​

​$$\sqrt{2- \sqrt3}$$

Solution:

Squaring,

($$\sqrt{2- \sqrt3}$$ )² = $$2- \sqrt3$$​​

Option (A):

​$$\frac{\sqrt6-\sqrt2}{2}$$ ​

​$$\left(\frac{\sqrt6-\sqrt2}{2}\right)^2$$=$$\frac{8 -2\sqrt {12}}{4}$$ = $$\frac{8- 4\sqrt 3}4= 2-\sqrt 3$$ 

Option (B):

​$$\frac{2-\sqrt3}{2}$$​​

​$$\left(\frac{2-\sqrt3}{2}\right)^2 = \frac{7 -4\sqrt3}4$$

Option (C):

$$\frac{\sqrt6-\sqrt3}{2}$$​

$$\left(\frac{\sqrt6-\sqrt3}{2}\right)^2$$= $$\frac{9 -6\sqrt {2}}{4}$$

​​Option (D):

​$$\frac{\sqrt2-\sqrt3}{2}$$

$$\left(\frac{\sqrt2-\sqrt3}{2}\right)^2$$= $$\frac{5-2\sqrt6}{4}$$​​​

Thus, option (A) is right.