Solve frac{3sqrt{12}}{4sqrt{7}}

$$\frac { 3 \sqrt { 12 } } { 4 \sqrt { 7 } }$$

Evaluate

$$\frac{3\sqrt{21}}{14}\approx 0.981980506$$

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}.

$$\frac{3\times 2\sqrt{3}}{4\sqrt{7}}$$

Multiply 3 and 2 to get 6.

$$\frac{6\sqrt{3}}{4\sqrt{7}}$$

Cancel out 2 in both numerator and denominator.

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

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

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

The square of \sqrt{7} is 7.

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

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

$$\frac{3\sqrt{21}}{2\times 7}$$

Multiply 2 and 7 to get 14.

$$\frac{3\sqrt{21}}{14}$$