Solve frac{sqrt{3}}{2}frac{sqrt{3}}{2}-(1/2)(1/2)

$$\frac{ \sqrt{ 3 } }{ 2 } \frac{ \sqrt{ 3 } }{ 2 } -( \frac{ 1 }{ 2 } )( \frac{ 1 }{ 2 } )$$

Evaluate

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

Solution Steps

Multiply \frac{\sqrt{3}}{2} and \frac{\sqrt{3}}{2} to get \left(\frac{\sqrt{3}}{2}\right)^{2}.

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

To raise \frac{\sqrt{3}}{2} to a power, raise both numerator and denominator to the power and then divide.

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

Multiply \frac{1}{2} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\times 1}{2\times 2}.

$$\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}-\frac{1}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Expand 2^{2}.

$$\frac{\left(\sqrt{3}\right)^{2}}{4}-\frac{1}{4}$$

Since \frac{\left(\sqrt{3}\right)^{2}}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(\sqrt{3}\right)^{2}-1}{4}$$

The square of \sqrt{3} is 3.

$$\frac{3}{2^{2}}-\frac{1}{4}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{3}{4}-\frac{1}{4}$$

Since \frac{3}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-1}{4}$$

Subtract 1 from 3 to get 2.

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

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

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

Factor

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