Solve frac{sqrt{21}}{sqrt{14}}=

$$\frac { \sqrt { 21 } } { \sqrt { 14 } } =$$

Evaluate

$$\frac{\sqrt{6}}{2}\approx 1.224744871$$

Solution Steps

Rationalize the denominator of \frac{\sqrt{21}}{\sqrt{14}} by multiplying numerator and denominator by \sqrt{14}.

$$\frac{\sqrt{21}\sqrt{14}}{\left(\sqrt{14}\right)^{2}}$$

The square of \sqrt{14} is 14.

$$\frac{\sqrt{21}\sqrt{14}}{14}$$

To multiply \sqrt{21} and \sqrt{14}, multiply the numbers under the square root.

$$\frac{\sqrt{294}}{14}$$

Factor 294=7^{2}\times 6. Rewrite the square root of the product \sqrt{7^{2}\times 6} as the product of square roots \sqrt{7^{2}}\sqrt{6}. Take the square root of 7^{2}.

$$\frac{7\sqrt{6}}{14}$$

Divide 7\sqrt{6} by 14 to get \frac{1}{2}\sqrt{6}.

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