Solve 2sqrt{2}*(-3sqrt{6})-frac{sqrt{3}}{4}

$$2 \sqrt { 2 } \cdot ( - 3 \sqrt { 6 } ) - \frac { \sqrt { 3 } } { 4 }$$

Evaluate

$$-\frac{49\sqrt{3}}{4}\approx -21.217622393$$

Solution Steps

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$2\sqrt{2}\left(-3\right)\sqrt{2}\sqrt{3}-\frac{\sqrt{3}}{4}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

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

Multiply 2 and 2 to get 4.

$$4\left(-3\right)\sqrt{3}-\frac{\sqrt{3}}{4}$$

Multiply 4 and -3 to get -12.

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

Combine -12\sqrt{3} and -\frac{\sqrt{3}}{4} to get -\frac{49}{4}\sqrt{3}.

$$-\frac{49}{4}\sqrt{3}$$