Solve frac{sqrt{12}}{sqrt{7}}

$$\frac{ \sqrt{ 12 } }{ \sqrt{ 7 } }$$

Evaluate

$$\frac{2\sqrt{21}}{7}\approx 1.309307341$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\frac{2\sqrt{3}}{\sqrt{7}}$$

Rationalize the denominator of \frac{2\sqrt{3}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{2\sqrt{3}\sqrt{7}}{\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$\frac{2\sqrt{3}\sqrt{7}}{7}$$

To multiply \sqrt{3} and \sqrt{7}, multiply the numbers under the square root.

$$\frac{2\sqrt{21}}{7}$$