Solve sqrt{1/3}divsqrt{1/9}

$$\sqrt { \frac { 1 } { 3 } } \div \sqrt { \frac { 1 } { 9 } }$$

Evaluate

$$\sqrt{3}\approx 1.732050808$$

Solution Steps

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

$$\frac{\frac{\sqrt{1}}{\sqrt{3}}}{\sqrt{\frac{1}{9}}}$$

Calculate the square root of 1 and get 1.

$$\frac{\frac{1}{\sqrt{3}}}{\sqrt{\frac{1}{9}}}$$

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

$$\frac{\frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}{\sqrt{\frac{1}{9}}}$$

The square of \sqrt{3} is 3.

$$\frac{\frac{\sqrt{3}}{3}}{\sqrt{\frac{1}{9}}}$$

Rewrite the square root of the division \frac{1}{9} as the division of square roots \frac{\sqrt{1}}{\sqrt{9}}. Take the square root of both numerator and denominator.

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

Divide \frac{\sqrt{3}}{3} by \frac{1}{3} by multiplying \frac{\sqrt{3}}{3} by the reciprocal of \frac{1}{3}.

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

Cancel out 3 and 3.

$$\sqrt{3}$$