Question

The square root of $7+3\sqrt{5}$ is

• A. $\frac{3+\sqrt{5}}{\sqrt{2}}$
• B. $\frac{3+\sqrt{5}}{\sqrt{3}}$
• C. $\frac{3+\sqrt{3}}{\sqrt{2}}$
• D. $\frac{5+\sqrt{5}}{\sqrt{2}}$

Answer 1

The correct option is A $\frac{3+\sqrt{5}}{\sqrt{2}}$

$7+3\sqrt{5}$
Multiply and divide by 2,
$=\frac{14+6\sqrt{5}}{2}=\frac{9+5+2\sqrt{45}}{2}$
$=\frac{(\sqrt{9}+\sqrt{5}{)}^2}{(\sqrt{2}{)}^2}$
$\sqrt{7+3\sqrt{5}}=\sqrt{\frac{(\sqrt{9}+\sqrt{5}{)}^2}{({\sqrt{2}}^2}}$
Ans is $\frac{(\sqrt{9}+\sqrt{5})}{\sqrt{2}}$