The value of √(5 + 2√6) is:
Show answer & explanation
Correct answer: B
Explanation
Using the identity (x + y)2 = x2 + y2 + 2xy:
\begin{align*} \sqrt{5 + 2\sqrt{6}} &= \sqrt{(3+2) + 2\sqrt{3 \times 2}} \\[2mm] \sqrt{5 + 2\sqrt{6}} &= \sqrt{(\sqrt{3})^2 + (\sqrt{2})^2 + 2(\sqrt{3})(\sqrt{2})} \\[2mm] \sqrt{5 + 2\sqrt{6}} &= \sqrt{(\sqrt{3} + \sqrt{2})^2} = \sqrt{3} + \sqrt{2} \end{align*}