Solve 1+1/2sqrt{7}

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

Evaluate

$$\frac{\sqrt{7}}{14}+1\approx 1.188982237$$

Solution Steps

Rationalize the denominator of \frac{1}{2\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$1+\frac{\sqrt{7}}{2\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$1+\frac{\sqrt{7}}{2\times 7}$$

Multiply 2 and 7 to get 14.

$$1+\frac{\sqrt{7}}{14}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{14}{14}.

$$\frac{14}{14}+\frac{\sqrt{7}}{14}$$

Since \frac{14}{14} and \frac{\sqrt{7}}{14} have the same denominator, add them by adding their numerators.

$$\frac{14+\sqrt{7}}{14}$$

Factor

$$\frac{\sqrt{7} + 14}{14} = 1.1889822365046137$$