​Find the positive square root of $$92-24 \sqrt{6-4 \sqrt{2}}$$​​

Correct option is A

Given: 

N = $$92 - 24\sqrt{6 - 4\sqrt2}$$  

Formula Used:

(A + B)²= A²+ B²+ 2 AB

(A - B)²= A²+ B²- 2 AB

Solution:

N = $$92 - 24\sqrt{6 - 4\sqrt2}$$   

= $$92 - 24\sqrt{2^2 + \sqrt{2}^2 - 2 \times2\sqrt2}$$   

= $$92 - 24\sqrt{(2 - \sqrt{2})^2}$$  

= $$92 - 24 (2 - \sqrt{2})$$  

= 92 - 48 + 24 $$\sqrt{2}$$ 

= 44 + 24 $$\sqrt{2}$$

= 6² + (2$$\sqrt{2}$$)² + (2 $$\times$$ 6 $$\times$$ 2$$\sqrt{2}$$)

= (6 + 2$$\sqrt{2}$$)²​

Therefore, $$\sqrt{N}$$ = (6 + 2$$\sqrt{2}$$)

Thus, the correct option is (a).