Solve frac{sqrt{3}}{2}*frac{sqrt{3}}{2}-frac{sqrt{2}}{2}*12/2

$$\frac { \sqrt { 3 } } { 2 } \cdot \frac { \sqrt { 3 } } { 2 } - \frac { \sqrt { 2 } } { 2 } \cdot \frac { 12 } { 2 }$$

Evaluate

$$\frac{3}{4}-3\sqrt{2}\approx -3.492640687$$

Solution Steps

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

$$\left(\frac{\sqrt{3}}{2}\right)^{2}-\frac{\sqrt{2}}{2}\times \frac{12}{2}$$

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

$$\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}-\frac{\sqrt{2}}{2}\times \frac{12}{2}$$

Divide 12 by 2 to get 6.

$$\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}-\frac{\sqrt{2}}{2}\times 6$$

Cancel out 2, the greatest common factor in 6 and 2.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply -3\sqrt{2} times \frac{2^{2}}{2^{2}}.

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

Since \frac{\left(\sqrt{3}\right)^{2}}{2^{2}} and \frac{-3\sqrt{2}\times 2^{2}}{2^{2}} have the same denominator, add them by adding their numerators.

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

The square of \sqrt{3} is 3.

$$\frac{3}{2^{2}}-3\sqrt{2}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{3}{4}-3\sqrt{2}$$

Factor

$$\frac{3 {(1 - 4 \sqrt{2})}}{4} = -3.4926406871192857$$