Solve frac{sqrt{24}}{sqrt{336}}

$$\frac { \sqrt { 24 } } { \sqrt { 336 } }$$

Evaluate

$$\frac{\sqrt{14}}{14}\approx 0.267261242$$

Solution Steps

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}.

$$\frac{2\sqrt{6}}{\sqrt{336}}$$

Factor 336=4^{2}\times 21. Rewrite the square root of the product \sqrt{4^{2}\times 21} as the product of square roots \sqrt{4^{2}}\sqrt{21}. Take the square root of 4^{2}.

$$\frac{2\sqrt{6}}{4\sqrt{21}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\sqrt{6}}{2\sqrt{21}}$$

Rationalize the denominator of \frac{\sqrt{6}}{2\sqrt{21}} by multiplying numerator and denominator by \sqrt{21}.

$$\frac{\sqrt{6}\sqrt{21}}{2\left(\sqrt{21}\right)^{2}}$$

The square of \sqrt{21} is 21.

$$\frac{\sqrt{6}\sqrt{21}}{2\times 21}$$

To multiply \sqrt{6} and \sqrt{21}, multiply the numbers under the square root.

$$\frac{\sqrt{126}}{2\times 21}$$

Multiply 2 and 21 to get 42.

$$\frac{\sqrt{126}}{42}$$

Factor 126=3^{2}\times 14. Rewrite the square root of the product \sqrt{3^{2}\times 14} as the product of square roots \sqrt{3^{2}}\sqrt{14}. Take the square root of 3^{2}.

$$\frac{3\sqrt{14}}{42}$$

Divide 3\sqrt{14} by 42 to get \frac{1}{14}\sqrt{14}.

$$\frac{1}{14}\sqrt{14}$$