Solve frac{sqrt{12}}{sqrt{60}}

$$\frac{ \sqrt{ 12 } }{ \sqrt{ 60 } }$$

Evaluate

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

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\frac{2\sqrt{3}}{\sqrt{60}}$$

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}.

$$\frac{2\sqrt{3}}{2\sqrt{15}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\sqrt{3}}{\sqrt{15}}$$

Rationalize the denominator of \frac{\sqrt{3}}{\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$\frac{\sqrt{3}\sqrt{15}}{\left(\sqrt{15}\right)^{2}}$$

The square of \sqrt{15} is 15.

$$\frac{\sqrt{3}\sqrt{15}}{15}$$

Factor 15=3\times 5. Rewrite the square root of the product \sqrt{3\times 5} as the product of square roots \sqrt{3}\sqrt{5}.

$$\frac{\sqrt{3}\sqrt{3}\sqrt{5}}{15}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{3\sqrt{5}}{15}$$

Divide 3\sqrt{5} by 15 to get \frac{1}{5}\sqrt{5}.

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