Solve frac{sqrt{5}}{5}divsqrt{3}

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

Evaluate

$$\frac{\sqrt{15}}{15}\approx 0.25819889$$

Solution Steps

Express \frac{\frac{\sqrt{5}}{5}}{\sqrt{3}} as a single fraction.

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

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

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

The square of \sqrt{3} is 3.

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

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

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

Multiply 5 and 3 to get 15.

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