Solve (frac{sqrt{7}+sqrt{3}}{2}+frac{sqrt{7}-sqrt{3}}{2})^2

$$( \frac { \sqrt { 7 } + \sqrt { 3 } } { 2 } + \frac { \sqrt { 7 } - \sqrt { 3 } } { 2 } ) ^ { 2 }$$

Evaluate

$$7$$

Short Solution Steps

Since \frac{\sqrt{7}+\sqrt{3}}{2} and \frac{\sqrt{7}-\sqrt{3}}{2} have the same denominator, add them by adding their numerators.

$$\left(\frac{\sqrt{7}+\sqrt{3}+\sqrt{7}-\sqrt{3}}{2}\right)^{2}$$

Do the calculations in \sqrt{7}+\sqrt{3}+\sqrt{7}-\sqrt{3}.

$$\left(\frac{2\sqrt{7}}{2}\right)^{2}$$

Cancel out 2 and 2.

$$\left(\sqrt{7}\right)^{2}$$

The square of \sqrt{7} is 7.

$$7$$

Factor

$$7$$