Question

The value of$\sqrt{\left(248+\sqrt{\left(52+\sqrt{144}\right)}\right)}$ is

• A. $14$
• B. $12$
• C. $16$
• D. $13$

Answer 1

The correct option is C

$16$

Explanation for the correct option:

Find the value of$\sqrt{\left(248+\sqrt{\left(52+\sqrt{144}\right)}\right)}$

$\begin{array}{rcl}\sqrt{\left(248+\sqrt{\left(52+\sqrt{144}\right)}\right)}& =& \sqrt{248+\sqrt{52+12}}\\ & =& \sqrt{248+\sqrt{64}}\\ & =& \sqrt{248+8}\\ & =& \sqrt{256}\\ & =& 16\\ \therefore \sqrt{\left(248+\sqrt{\left(52+\sqrt{144}\right)}\right)}& =& 16\end{array}$

Hence, the correct option is C.