Solve sqrt{1/3}divsqrt{3}

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

Evaluate

$$\frac{1}{3}\approx 0.333333333$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{3}} as the division of square roots \frac{\sqrt{1}}{\sqrt{3}}.

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

Calculate the square root of 1 and get 1.

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

Rationalize the denominator of \frac{1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

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

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

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

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

The square of \sqrt{3} is 3.

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

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

$$\frac{3}{3\times 3}$$

Multiply 3 and 3 to get 9.

$$\frac{3}{9}$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{1}{3}$$

Factor

$$\frac{1}{3} = 0.3333333333333333$$