Solve -frac{2sqrt{5}}{3}*9sqrt{6}divsqrt{12}=

$$- \frac { 2 \sqrt { 5 } } { 3 } \times 9 \sqrt { 6 } \div \sqrt { 12 } =$$

Evaluate

$$-3\sqrt{10}\approx -9.486832981$$

Solution Steps

Cancel out 3, the greatest common factor in 9 and 3.

$$\frac{-3\times 2\sqrt{5}\sqrt{6}}{\sqrt{12}}$$

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}.

$$\frac{-3\times 2\sqrt{5}\sqrt{6}}{2\sqrt{3}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-3\sqrt{5}\sqrt{6}}{\sqrt{3}}$$

Rationalize the denominator of \frac{-3\sqrt{5}\sqrt{6}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{-3\sqrt{5}\sqrt{6}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{-3\sqrt{5}\sqrt{6}\sqrt{3}}{3}$$

To multiply \sqrt{5} and \sqrt{6}, multiply the numbers under the square root.

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

Factor 30=3\times 10. Rewrite the square root of the product \sqrt{3\times 10} as the product of square roots \sqrt{3}\sqrt{10}.

$$\frac{-3\sqrt{3}\sqrt{10}\sqrt{3}}{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{-3\times 3\sqrt{10}}{3}$$

Cancel out 3 and 3.

$$-3\sqrt{10}$$