Solve sqrt{3/20}

$$\sqrt { \frac { 3 } { 20 } }$$

Evaluate

$$\frac{\sqrt{15}}{10}\approx 0.387298335$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{3}{20}} as the division of square roots \frac{\sqrt{3}}{\sqrt{20}}.

$$\frac{\sqrt{3}}{\sqrt{20}}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$\frac{\sqrt{3}}{2\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{3}}{2\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{3}\sqrt{5}}{2\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{3}\sqrt{5}}{2\times 5}$$

To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{15}}{2\times 5}$$

Multiply 2 and 5 to get 10.

$$\frac{\sqrt{15}}{10}$$