​Find the positive square root of $$207-54 \sqrt{6+4 \sqrt{2}}$$​

Correct option is D

Given: 

N = $$207 - 54 \sqrt{6 + 4 \sqrt{2}}$$  

Formula Used:

(A + B )² = A² + B² + 2 AB

(A - B)² = A² + B² - 2 AB

Solution:

N = $$207 - 54 \sqrt{6 + 4 \sqrt{2}}$$  

= $$207 - 54 \sqrt{2^2 + (\sqrt{2})^2 + 2 \times 2 \sqrt{2}}$$   

= $$207 - 54 \sqrt{(2 + \sqrt{2})^2}$$

= $$207 - 54 (2 + \sqrt{2})$$

= $$207 - 108 - 54 \sqrt{2}$$

= $$99 - 54 \sqrt{2}$$

= $$9^2 + (3\sqrt{2})^2 - 2 \times 9 \times 3 \sqrt{2}$$

N = $$(9 - 3\sqrt{2})^2$$

​=> $$\sqrt{N} = 9 - 3 \sqrt{2}$$  

Thus, the correct option is (d)