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

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

Evaluate

$$\sqrt{3}-1\approx 0.732050808$$

Solution Steps

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

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

Combine \frac{\sqrt{3}}{2} and \frac{\sqrt{3}}{2} to get \sqrt{3}.

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

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

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

Express 3\times \frac{\left(\sqrt{3}\right)^{2}}{3^{2}} as a single fraction.

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

Cancel out 3 in both numerator and denominator.

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

The square of \sqrt{3} is 3.

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

Divide 3 by 3 to get 1.

$$\sqrt{3}-1$$

Factor

$$\sqrt{3} - 1 = 0.732050808$$