Solve frac{sqrt{3}}{3}tan30^circ+sqrt{3}tan60^circ

$$\frac { \sqrt { 3 } } { 3 } \tan 30 ^ { \circ } + \sqrt { 3 } \tan 60 ^ { \circ }$$

Evaluate

$$\frac{10}{3}\approx 3.333333333$$

Solution Steps

Get the value of \tan(30) from trigonometric values table.

$$\frac{\sqrt{3}}{3}\times \frac{\sqrt{3}}{3}+\sqrt{3}\tan(60)$$

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

$$\left(\frac{\sqrt{3}}{3}\right)^{2}+\sqrt{3}\tan(60)$$

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

$$\frac{\left(\sqrt{3}\right)^{2}}{3^{2}}+\sqrt{3}\tan(60)$$

Get the value of \tan(60) from trigonometric values table.

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

Multiply \sqrt{3} and \sqrt{3} to get 3.

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

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

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

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

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

The square of \sqrt{3} is 3.

$$\frac{3}{3^{2}}+3$$

Calculate 3 to the power of 2 and get 9.

$$\frac{3}{9}+3$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{1}{3}+3$$

Add \frac{1}{3} and 3 to get \frac{10}{3}.

$$\frac{10}{3}$$