Solve sqrt{1/24}divsqrt{2/3}

$$\sqrt { \frac { 1 } { 24 } } \div \sqrt { \frac { 2 } { 3 } }$$

Evaluate

$$\frac{1}{4}=0.25$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{24}} as the division of square roots \frac{\sqrt{1}}{\sqrt{24}}.

$$\frac{\frac{\sqrt{1}}{\sqrt{24}}}{\sqrt{\frac{2}{3}}}$$

Calculate the square root of 1 and get 1.

$$\frac{\frac{1}{\sqrt{24}}}{\sqrt{\frac{2}{3}}}$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

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

Rationalize the denominator of \frac{1}{2\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

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

The square of \sqrt{6} is 6.

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

Multiply 2 and 6 to get 12.

$$\frac{\frac{\sqrt{6}}{12}}{\sqrt{\frac{2}{3}}}$$

Rewrite the square root of the division \sqrt{\frac{2}{3}} as the division of square roots \frac{\sqrt{2}}{\sqrt{3}}.

$$\frac{\frac{\sqrt{6}}{12}}{\frac{\sqrt{2}}{\sqrt{3}}}$$

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

$$\frac{\frac{\sqrt{6}}{12}}{\frac{\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}$$

The square of \sqrt{3} is 3.

$$\frac{\frac{\sqrt{6}}{12}}{\frac{\sqrt{2}\sqrt{3}}{3}}$$

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

$$\frac{\frac{\sqrt{6}}{12}}{\frac{\sqrt{6}}{3}}$$

Divide \frac{\sqrt{6}}{12} by \frac{\sqrt{6}}{3} by multiplying \frac{\sqrt{6}}{12} by the reciprocal of \frac{\sqrt{6}}{3}.

$$\frac{\sqrt{6}\times 3}{12\sqrt{6}}$$

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

$$\frac{1}{4}$$

Factor

$$\frac{1}{2 ^ {2}} = 0.25$$