Solve frac{sqrt{3}+1}{2}*frac{sqrt{3}-1}{2}

$$\frac{ \sqrt{ 3 } +1 }{ 2 } \times \frac{ \sqrt{ 3 } -1 }{ 2 }$$

Evaluate

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

Solution Steps

Multiply \frac{\sqrt{3}+1}{2} times \frac{\sqrt{3}-1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)}{2\times 2}$$

Consider \left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(\sqrt{3}\right)^{2}-1^{2}}{2\times 2}$$

The square of \sqrt{3} is 3.

$$\frac{3-1^{2}}{2\times 2}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{3-1}{2\times 2}$$

Subtract 1 from 3 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

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