Solve frac{12sqrt{2}}{sqrt{3}}

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

Evaluate

$$4\sqrt{6}\approx 9.797958971$$

Solution Steps

Rationalize the denominator of \frac{12\sqrt{2}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

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

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

Divide 12\sqrt{6} by 3 to get 4\sqrt{6}.

$$4\sqrt{6}$$