Solve frac{sqrt{3}}{2}quad2/sqrt{13}

$$\frac { \sqrt { 3 } } { 2 } \quad \frac { 2 } { \sqrt { 13 } }$$

Evaluate

$$\frac{\sqrt{39}}{13}\approx 0.480384461$$

Solution Steps

Rationalize the denominator of \frac{2}{\sqrt{13}} by multiplying numerator and denominator by \sqrt{13}.

$$\frac{\sqrt{3}}{2}\times \frac{2\sqrt{13}}{\left(\sqrt{13}\right)^{2}}$$

The square of \sqrt{13} is 13.

$$\frac{\sqrt{3}}{2}\times \frac{2\sqrt{13}}{13}$$

Multiply \frac{\sqrt{3}}{2} times \frac{2\sqrt{13}}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{3}\times 2\sqrt{13}}{2\times 13}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\sqrt{3}\sqrt{13}}{13}$$

To multiply \sqrt{3} and \sqrt{13}, multiply the numbers under the square root.

$$\frac{\sqrt{39}}{13}$$