Solve frac{2*frac{13sqrt{3}}{2}}{2sqrt{13}}

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

Evaluate

$$\frac{\sqrt{39}}{2}\approx 3.122498999$$

Solution Steps

Cancel out 2 and 2.

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

Rationalize the denominator of \frac{13\sqrt{3}}{2\sqrt{13}} by multiplying numerator and denominator by \sqrt{13}.

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

The square of \sqrt{13} is 13.

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

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

$$\frac{13\sqrt{39}}{2\times 13}$$

Multiply 2 and 13 to get 26.

$$\frac{13\sqrt{39}}{26}$$

Divide 13\sqrt{39} by 26 to get \frac{1}{2}\sqrt{39}.

$$\frac{1}{2}\sqrt{39}$$