Solve 4sqrt{48}*(-2/3sqrt{0.5})*6sqrt{6}

$$4 \sqrt { 48 } \times ( - \frac { 2 } { 3 } \sqrt { 0.5 } ) \times 6 \sqrt { 6 }$$

Evaluate

$$-192$$

Solution Steps

Factor 48=6\times 8. Rewrite the square root of the product \sqrt{6\times 8} as the product of square roots \sqrt{6}\sqrt{8}.

$$4\times 6\sqrt{6}\sqrt{8}\left(-\frac{2}{3}\right)\sqrt{0.5}\sqrt{6}$$

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

$$4\times 6\times 6\left(-\frac{2}{3}\right)\sqrt{0.5}\sqrt{8}$$

Multiply 4 and 6 to get 24.

$$24\times 6\left(-\frac{2}{3}\right)\sqrt{0.5}\sqrt{8}$$

Multiply 24 and 6 to get 144.

$$144\left(-\frac{2}{3}\right)\sqrt{0.5}\sqrt{8}$$

Express 144\left(-\frac{2}{3}\right) as a single fraction.

$$\frac{144\left(-2\right)}{3}\sqrt{0.5}\sqrt{8}$$

Multiply 144 and -2 to get -288.

$$\frac{-288}{3}\sqrt{0.5}\sqrt{8}$$

Divide -288 by 3 to get -96.

$$-96\sqrt{0.5}\sqrt{8}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$-96\sqrt{0.5}\times 2\sqrt{2}$$

Multiply -96 and 2 to get -192.

$$-192\sqrt{0.5}\sqrt{2}$$

To multiply \sqrt{0.5} and \sqrt{2}, multiply the numbers under the square root.

$$-192\sqrt{1}$$

Calculate the square root of 1 and get 1.

$$-192$$

Factor

$$-192$$