Solve frac{2sqrt{13}}{9sqrt{5}}

$$\frac { 2 \sqrt { 13 } } { 9 \sqrt { 5 } }$$

Evaluate

$$\frac{2\sqrt{65}}{45}\approx 0.358322567$$

Solution Steps

Rationalize the denominator of \frac{2\sqrt{13}}{9\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{2\sqrt{13}\sqrt{5}}{9\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{2\sqrt{13}\sqrt{5}}{9\times 5}$$

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

$$\frac{2\sqrt{65}}{9\times 5}$$

Multiply 9 and 5 to get 45.

$$\frac{2\sqrt{65}}{45}$$