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Simplify the expression: (9+45)\sqrt{(9 + 4\sqrt{5})}(9+45​)​​​
Question

Simplify the expression: (9+45)\sqrt{(9 + 4\sqrt{5})}​​

A.

52 \sqrt{5} - 2\\

B.

3 + 5 \sqrt{5}

C.

2 + 6 \sqrt{6}

D.

3 + 4 \sqrt{4}

Correct option is A

Given:
(9+45)\sqrt{(9 + 4\sqrt{5})} 
Formula Used:
(a − b)² = a² + b² − 2ab
Solution:
(9+45)=(5+4+45)=(52+22+2×2×5)=(5+2)2=5+2\sqrt{(9 + 4\sqrt{5})}\\= \sqrt{(5 + 4 + 4\sqrt{5})}\\= \sqrt{(\sqrt{5}^2 + 2^2 + 2 \times 2 \times \sqrt{5})}\\= \sqrt{(\sqrt{5} + 2)^2}\\= \sqrt{5} + 2\\​​

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