The value of $$\sqrt{10 + \sqrt{221 + \sqrt{12 + \sqrt{16}}}}$$ is:​

Correct option is C

To solve:

​$$\sqrt{10 + \sqrt{221 + \sqrt{12 + \sqrt{16}}}}$$

Solution:

​$$\begin{aligned}&\sqrt{10 + \sqrt{221 + \sqrt{12 + \sqrt{16}}}} \\&\Rightarrow \sqrt{10 + \sqrt{221 + \sqrt{12 + 4}}} \\&\Rightarrow \sqrt{10 + \sqrt{221 + \sqrt{16}}} \\&\Rightarrow \sqrt{10 + \sqrt{221 + 4}} \\&\Rightarrow \sqrt{10 + \sqrt{225}} \\&\Rightarrow \sqrt{10 + 15} \\&\Rightarrow \sqrt{25} = 5\end{aligned}$$​​

Hence,  option (c) is the  correct answer.