Solve frac{6sqrt{13}}{4sqrt{5}}

$$\frac{ 6 \sqrt{ 13 } }{ 4 \sqrt{ 5 } }$$

Evaluate

$$\frac{3\sqrt{65}}{10}\approx 2.418677324$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{3\sqrt{13}}{2\sqrt{5}}$$

Rationalize the denominator of \frac{3\sqrt{13}}{2\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{3\sqrt{13}\sqrt{5}}{2\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{3\sqrt{13}\sqrt{5}}{2\times 5}$$

To multiply \sqrt{13} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{3\sqrt{65}}{2\times 5}$$

Multiply 2 and 5 to get 10.

$$\frac{3\sqrt{65}}{10}$$