Question

What is the positive square root of $7+4\sqrt{3}$?

• A. $\sqrt{3}-1$
• B. $\sqrt{3}+1$
• C. $\sqrt{3}-2$
• D. $\sqrt{3}+2$

Answer 1

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

$7+4\sqrt{3}=4+3+4\sqrt{3}=2^2+{\left(\sqrt{3}\right)}^2+2\times 2\times \sqrt{3}={(2+\sqrt{3})}^2$

So $2+\sqrt{3}$ is positive square root of $7+4\sqrt{3}$