Question

Find the square root of $7+4\sqrt{3}$

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

Answer 1

The correct option is A $2+\sqrt{3}$

Let $\sqrt{7+4\sqrt{3}}=\sqrt{x}+\sqrt{y}$
Squaring both the sides $7+4\sqrt{3}=x+y+2\sqrt{xy}$
$\Rightarrow x+y=7$ and $\sqrt{xy}=2\sqrt{3}=\sqrt{12}$
$\Rightarrow xy=12$
By solving we get $x=4$ and $y=3$
$\sqrt{x}+\sqrt{y}=\sqrt{4}+\sqrt{3}=2+\sqrt{3}$