Question

The positive square root of $7+\sqrt{48}$ is

• A. $7+2\sqrt{3}$
• B. $7+\sqrt{3}$
• C. $2+\sqrt{3}$
• D. $3+\sqrt{2}$

Answer 1

The correct option is C

$2+\sqrt{3}$

$7+\sqrt{48}=7+\sqrt{4\times 12}$

$=7+2\sqrt{12}$

$=4+3+2\sqrt{4\times 3}$

$=(\sqrt{4}{)}^2+(\sqrt{3}{)}^2+2\times (\sqrt{4}\times \sqrt{3})$

$=(\sqrt{4}+\sqrt{3}{)}^2$

$\therefore Squareroot=\sqrt{4}+\sqrt{3}$

$=2+\sqrt{3}$