Solve sqrt{3/5}divsqrt{5}

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

Evaluate

$$\frac{\sqrt{3}}{5}\approx 0.346410162$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{3}{5}} as the division of square roots \frac{\sqrt{3}}{\sqrt{5}}.

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

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

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

The square of \sqrt{5} is 5.

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

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

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

Express \frac{\frac{\sqrt{15}}{5}}{\sqrt{5}} as a single fraction.

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

Rationalize the denominator of \frac{\sqrt{15}}{5\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{15}\sqrt{5}}{5\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

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

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

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

Multiply \sqrt{5} and \sqrt{5} to get 5.

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

Multiply 5 and 5 to get 25.

$$\frac{5\sqrt{3}}{25}$$

Divide 5\sqrt{3} by 25 to get \frac{1}{5}\sqrt{3}.

$$\frac{1}{5}\sqrt{3}$$