​If X = $$\sqrt{(1+\frac{\sqrt3}{2})}+\sqrt{(1-\frac{\sqrt3}{2})}$$ then the simplified value of X will be:​​

Correct option is A

Given:​​

X =$$\sqrt{(1+\frac{\sqrt3}{2})}+\sqrt{(1-\frac{\sqrt3}{2})}$$

Formula Used:

(a + b)² = a² + b² + 2ab

a² - b² = (a + b) (a - b)

​Solution:​

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

Squaring,

​$$X^2=\left(\sqrt{(1+\frac{\sqrt3}{2})}+\sqrt{(1-\frac{\sqrt3}{2})}\right)^2$$

$$X^2=1+\frac{\sqrt3}{2}+1-\frac{\sqrt3}{2}+2\sqrt{1-\frac{3}{4}}$$

​​​$$X^2=2+2\sqrt{\frac{4-3}{4}}$$

​​$$X^2=2+2\times\frac 12$$

$$X^2=2+1$$

X²​ = 3

Now, 

X = $$\sqrt 3$$​​