Solve frac{sqrt{7}+sqrt{5}}{2}*frac{sqrt{7}-sqrt{5}}{2}

$$\frac{ \sqrt{ 7 } + \sqrt{ 5 } }{ 2 } \times \frac{ \sqrt{ 7 } - \sqrt{ 5 } }{ 2 }$$

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

Multiply \frac{\sqrt{7}+\sqrt{5}}{2} times \frac{\sqrt{7}-\sqrt{5}}{2} by multiplying numerator times numerator and denominator times denominator.

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

Consider \left(\sqrt{7}+\sqrt{5}\right)\left(\sqrt{7}-\sqrt{5}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

The square of \sqrt{7} is 7.

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

The square of \sqrt{5} is 5.

$$\frac{7-5}{2\times 2}$$

Subtract 5 from 7 to get 2.

$$\frac{2}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{2}{4}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$