Question

Find the square root of $\frac{2+\sqrt{3}}{2}$

• A. $\frac{1+\sqrt{3}}{4}$
• B. $\frac{1+\sqrt{3}}{2}$
• C. $\frac{2+\sqrt{5}}{2}$
• D. $\frac{1+\sqrt{1}}{2}$

Answer 1

The correct option is B $\frac{1+\sqrt{3}}{2}$

Given,$\frac{2+\sqrt{3}}{2}$
Multiply and divide by $2$

$=\frac{4+2\sqrt{3}}{4}=\frac{1+3+2\sqrt{3}}{4}$

$=\frac{(1+\sqrt{3}{)}^2}{2^2}$

$\sqrt{\frac{2+\sqrt{3}}{2}}=\sqrt{\frac{(1+\sqrt{3}{)}^2}{2^2}}$

Answer is $\frac{(1+\sqrt{3})}{2}$