Solve 2sqrt{1/3}div2sqrt{3}

$$2 \sqrt { \frac { 1 } { 3 } } \div 2 \sqrt { 3 }$$

Evaluate

$$1$$

Solution Steps

Cancel out 2 and 2.

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

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

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{3} is 3.

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

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

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

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

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

Divide 3 by 3 to get 1.

$$1$$

Factor

$$1$$