Question

If $x=7+4\sqrt{3}$, the value of $\sqrt{x}$ is ________.

• A. $4$
• B. $4+\sqrt{3}$
• C. $2+\sqrt{3}$
• D. $2-\sqrt{3}$

Answer 1

The correct option is C

$2+\sqrt{3}$

$x=7+4\sqrt{3}$

$x=4+3+4\sqrt{3}$

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

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

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

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

$\sqrt{x}=2+\sqrt{3}$