Evaluate: $$\sqrt{\left(76 + \sqrt{\left(21 + \sqrt{\left(9 + \sqrt{\left(40 + \sqrt{\left(81\right)}\right)}\right)}\right)}\right)}$$​​

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Correct option is A

Given:

$$\sqrt{\left(76 + \sqrt{\left(21 + \sqrt{\left(9 + \sqrt{\left(40 + \sqrt{\left(81\right)}\right)}\right)}\right)}\right)}$$ 

Solution:

$$\sqrt{\left(76 + \sqrt{\left(21 + \sqrt{\left(9 + \sqrt{\left(40 + \sqrt{\left(81\right)}\right)}\right)}\right)}\right)} \\ \ \\ = \sqrt{\left(76 + \sqrt{\left(21 + \sqrt{\left(9 + \sqrt{\left(40 + 9\right)}\right)}\right)}\right)} \\ \ \\ = \sqrt{\left(76 + \sqrt{\left(21 + \sqrt{\left(9 +7\right)}\right)}\right)} \\ \ \\ = \sqrt{\left(76 + \sqrt{\left(21 + 4\right)}\right)} \\ \ \\ = \sqrt{\left(76 + 5\right)} \\ \ \\ = 9$$​