Solve [1/2(sqrt{7}+sqrt{5})-1/2(sqrt{7}-sqrt{5})]^2

$$[ \frac { 1 } { 2 } ( \sqrt { 7 } + \sqrt { 5 } ) - \frac { 1 } { 2 } ( \sqrt { 7 } - \sqrt { 5 } ) ] ^ { 2 }$$

Evaluate

$$5$$

Solution Steps

Use the distributive property to multiply \frac{1}{2} by \sqrt{7}+\sqrt{5}.

$$\left(\frac{1}{2}\sqrt{7}+\frac{1}{2}\sqrt{5}-\frac{1}{2}\left(\sqrt{7}-\sqrt{5}\right)\right)^{2}$$

Use the distributive property to multiply -\frac{1}{2} by \sqrt{7}-\sqrt{5}.

$$\left(\frac{1}{2}\sqrt{7}+\frac{1}{2}\sqrt{5}-\frac{1}{2}\sqrt{7}+\frac{1}{2}\sqrt{5}\right)^{2}$$

Combine \frac{1}{2}\sqrt{7} and -\frac{1}{2}\sqrt{7} to get 0.

$$\left(\frac{1}{2}\sqrt{5}+\frac{1}{2}\sqrt{5}\right)^{2}$$

Combine \frac{1}{2}\sqrt{5} and \frac{1}{2}\sqrt{5} to get \sqrt{5}.

$$\left(\sqrt{5}\right)^{2}$$

The square of \sqrt{5} is 5.

$$5$$

Factor

$$5$$