Solve 1/sqrt{3}+2sqrt{7}=

$$\frac { 1 } { \sqrt { 3 } } + 2 \sqrt { 7 } =$$

Evaluate

$$\frac{\sqrt{3}}{3}+2\sqrt{7}\approx 5.868852891$$

Short Solution Steps

Rationalize the denominator of \frac{1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}+2\sqrt{7}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{3}}{3}+2\sqrt{7}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2\sqrt{7} times \frac{3}{3}.

$$\frac{\sqrt{3}}{3}+\frac{3\times 2\sqrt{7}}{3}$$

Since \frac{\sqrt{3}}{3} and \frac{3\times 2\sqrt{7}}{3} have the same denominator, add them by adding their numerators.

$$\frac{\sqrt{3}+3\times 2\sqrt{7}}{3}$$

Do the multiplications in \sqrt{3}+3\times 2\sqrt{7}.

$$\frac{\sqrt{3}+6\sqrt{7}}{3}$$