Solve 1+2/2sqrt{3}=

$$1 + \frac { 2 } { 2 \sqrt { 3 } } =$$

Evaluate

$$\frac{\sqrt{3}}{3}+1\approx 1.577350269$$

Solution Steps

Rationalize the denominator of \frac{2}{2\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

Cancel out 2 in both numerator and denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{3}{3}.

$$\frac{3}{3}+\frac{\sqrt{3}}{3}$$

Since \frac{3}{3} and \frac{\sqrt{3}}{3} have the same denominator, add them by adding their numerators.

$$\frac{3+\sqrt{3}}{3}$$