Solve frac{sqrt{15}}{sqrt{60}}

$$\frac { \sqrt { 15 } } { \sqrt { 60 } }$$

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

Factor 60=2^{2}\times 15. Rewrite the square root of the product \sqrt{2^{2}\times 15} as the product of square roots \sqrt{2^{2}}\sqrt{15}. Take the square root of 2^{2}.

$$\frac{\sqrt{15}}{2\sqrt{15}}$$

Rationalize the denominator of \frac{\sqrt{15}}{2\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$\frac{\sqrt{15}\sqrt{15}}{2\left(\sqrt{15}\right)^{2}}$$

The square of \sqrt{15} is 15.

$$\frac{\sqrt{15}\sqrt{15}}{2\times 15}$$

Multiply \sqrt{15} and \sqrt{15} to get 15.

$$\frac{15}{2\times 15}$$

Multiply 2 and 15 to get 30.

$$\frac{15}{30}$$

Reduce the fraction \frac{15}{30} to lowest terms by extracting and canceling out 15.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$