Solve frac{sqrt{13}}{sqrt{65}}

$$\frac { \sqrt { 13 } } { \sqrt { 65 } }$$

Evaluate

$$\frac{\sqrt{5}}{5}\approx 0.447213595$$

Solution Steps

Rationalize the denominator of \frac{\sqrt{13}}{\sqrt{65}} by multiplying numerator and denominator by \sqrt{65}.

$$\frac{\sqrt{13}\sqrt{65}}{\left(\sqrt{65}\right)^{2}}$$

The square of \sqrt{65} is 65.

$$\frac{\sqrt{13}\sqrt{65}}{65}$$

Factor 65=13\times 5. Rewrite the square root of the product \sqrt{13\times 5} as the product of square roots \sqrt{13}\sqrt{5}.

$$\frac{\sqrt{13}\sqrt{13}\sqrt{5}}{65}$$

Multiply \sqrt{13} and \sqrt{13} to get 13.

$$\frac{13\sqrt{5}}{65}$$

Divide 13\sqrt{5} by 65 to get \frac{1}{5}\sqrt{5}.

$$\frac{1}{5}\sqrt{5}$$