Question

$\left(4+\sqrt{7}\right)$ when expressed as a perfect square, is equal to:

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is B

$\begin{array}{c}\left(4+\sqrt{7}\right)=\frac{1}{2}\left[8+2\sqrt{7}\right]=\frac{1}{2}\left[{\left(\sqrt{7}\right)}^2+2\sqrt{7}+{\left(1\right)}^2\right]=\frac{1}{2}{\left(\sqrt{7}+1\right)}^2\\ ={\left[\frac{1}{\sqrt{2}}\left(\sqrt{7}+1\right)\right]}^2\end{array}$