Evaluate:

​$$\sqrt{\left(2 + \sqrt{\left(39 + \sqrt{\left(97 + \sqrt{\left(5 + \sqrt{\left(16\right)}\right)}\right)}\right)}\right)}$$​​

Correct option is C

Given:

​$$\sqrt{\left(2 + \sqrt{\left(39 + \sqrt{\left(97 + \sqrt{\left(5 + \sqrt{\left(16\right)}\right)}\right)}\right)}\right)}$$​​

Solution: 

​$$\sqrt{\left(2 + \sqrt{\left(39 + \sqrt{\left(97 + \sqrt{\left(5 + \sqrt{\left(16\right)}\right)}\right)}\right)}\right)} \\ \ \\ =\sqrt{\left(2 + \sqrt{\left(39 + \sqrt{\left(97 + \sqrt{\left(5 + 4\right)}\right)}\right)}\right)}\\ \ \\ =\sqrt{\left(2 + \sqrt{\left(39 + \sqrt{\left(97 + 3\right)}\right)}\right)}\\ \ \\ =\sqrt{\left(2 + \sqrt{\left(39 + 10\right)}\right)}\\ \ \\ =\sqrt{\left(2 + 7\right)}\\ \ \\ =\sqrt{\left(9\right)} \\ \ \\ = 3$$ 

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