Solve frac{-12sqrt{30}}{3sqrt{6}}

$$\frac { - 12 \sqrt { 30 } } { 3 \sqrt { 6 } }$$

Evaluate

$$-4\sqrt{5}\approx -8.94427191$$

Solution Steps

Cancel out 3 in both numerator and denominator.

$$\frac{-4\sqrt{30}}{\sqrt{6}}$$

Rationalize the denominator of \frac{-4\sqrt{30}}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{-4\sqrt{30}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{-4\sqrt{30}\sqrt{6}}{6}$$

Factor 30=6\times 5. Rewrite the square root of the product \sqrt{6\times 5} as the product of square roots \sqrt{6}\sqrt{5}.

$$\frac{-4\sqrt{6}\sqrt{5}\sqrt{6}}{6}$$

Multiply \sqrt{6} and \sqrt{6} to get 6.

$$\frac{-4\times 6\sqrt{5}}{6}$$

Cancel out 6 and 6.

$$-4\sqrt{5}$$