Solve 1/2*frac{sqrt{26}+sqrt{6}}{2}*frac{sqrt{26}-sqrt{6}}{2}

$$\frac { 1 } { 2 } \times \frac { \sqrt { 26 } + \sqrt { 6 } } { 2 } \times \frac { \sqrt { 26 } - \sqrt { 6 } } { 2 }$$

Evaluate

$$\frac{5}{2}=2.5$$

Solution Steps

Multiply \frac{1}{2} times \frac{\sqrt{26}+\sqrt{6}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{26}+\sqrt{6}}{2\times 2}\times \frac{\sqrt{26}-\sqrt{6}}{2}$$

Multiply \frac{\sqrt{26}+\sqrt{6}}{2\times 2} times \frac{\sqrt{26}-\sqrt{6}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(\sqrt{26}+\sqrt{6}\right)\left(\sqrt{26}-\sqrt{6}\right)}{2\times 2\times 2}$$

Consider \left(\sqrt{26}+\sqrt{6}\right)\left(\sqrt{26}-\sqrt{6}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(\sqrt{26}\right)^{2}-\left(\sqrt{6}\right)^{2}}{2\times 2\times 2}$$

The square of \sqrt{26} is 26.

$$\frac{26-\left(\sqrt{6}\right)^{2}}{2\times 2\times 2}$$

The square of \sqrt{6} is 6.

$$\frac{26-6}{2\times 2\times 2}$$

Subtract 6 from 26 to get 20.

$$\frac{20}{2\times 2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{20}{4\times 2}$$

Multiply 4 and 2 to get 8.

$$\frac{20}{8}$$

Reduce the fraction \frac{20}{8} to lowest terms by extracting and canceling out 4.

$$\frac{5}{2}$$

Factor

$$\frac{5}{2} = 2\frac{1}{2} = 2.5$$