Solve sqrt{22/3}divsqrt{1/6}

$$\sqrt { 2 \frac { 2 } { 3 } } \div \sqrt { \frac { 1 } { 6 } }$$

Evaluate

$$4$$

Solution Steps

Multiply 2 and 3 to get 6.

$$\frac{\sqrt{\frac{6+2}{3}}}{\sqrt{\frac{1}{6}}}$$

Add 6 and 2 to get 8.

$$\frac{\sqrt{\frac{8}{3}}}{\sqrt{\frac{1}{6}}}$$

Rewrite the square root of the division \sqrt{\frac{8}{3}} as the division of square roots \frac{\sqrt{8}}{\sqrt{3}}.

$$\frac{\frac{\sqrt{8}}{\sqrt{3}}}{\sqrt{\frac{1}{6}}}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{\frac{2\sqrt{2}}{\sqrt{3}}}{\sqrt{\frac{1}{6}}}$$

Rationalize the denominator of \frac{2\sqrt{2}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\frac{2\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}{\sqrt{\frac{1}{6}}}$$

The square of \sqrt{3} is 3.

$$\frac{\frac{2\sqrt{2}\sqrt{3}}{3}}{\sqrt{\frac{1}{6}}}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\frac{2\sqrt{6}}{3}}{\sqrt{\frac{1}{6}}}$$

Rewrite the square root of the division \sqrt{\frac{1}{6}} as the division of square roots \frac{\sqrt{1}}{\sqrt{6}}.

$$\frac{\frac{2\sqrt{6}}{3}}{\frac{\sqrt{1}}{\sqrt{6}}}$$

Calculate the square root of 1 and get 1.

$$\frac{\frac{2\sqrt{6}}{3}}{\frac{1}{\sqrt{6}}}$$

Rationalize the denominator of \frac{1}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{\frac{2\sqrt{6}}{3}}{\frac{\sqrt{6}}{\left(\sqrt{6}\right)^{2}}}$$

The square of \sqrt{6} is 6.

$$\frac{\frac{2\sqrt{6}}{3}}{\frac{\sqrt{6}}{6}}$$

Divide \frac{2\sqrt{6}}{3} by \frac{\sqrt{6}}{6} by multiplying \frac{2\sqrt{6}}{3} by the reciprocal of \frac{\sqrt{6}}{6}.

$$\frac{2\sqrt{6}\times 6}{3\sqrt{6}}$$

Cancel out 3\sqrt{6} in both numerator and denominator.

$$2\times 2$$

Multiply 2 and 2 to get 4.

$$4$$

Factor

$$2^{2}$$