Solve sqrt{13/180}

$$\sqrt { \frac { 13 } { 180 } }$$

Evaluate

$$\frac{\sqrt{65}}{30}\approx 0.268741925$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{13}{180}} as the division of square roots \frac{\sqrt{13}}{\sqrt{180}}.

$$\frac{\sqrt{13}}{\sqrt{180}}$$

Factor 180=6^{2}\times 5. Rewrite the square root of the product \sqrt{6^{2}\times 5} as the product of square roots \sqrt{6^{2}}\sqrt{5}. Take the square root of 6^{2}.

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

Rationalize the denominator of \frac{\sqrt{13}}{6\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{13}\sqrt{5}}{6\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

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

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

$$\frac{\sqrt{65}}{6\times 5}$$

Multiply 6 and 5 to get 30.

$$\frac{\sqrt{65}}{30}$$