Solve (-3/4):(-frac{sqrt{27}}{8})*6sqrt{3}

$$( - \frac { 3 } { 4 } ) : ( - \frac { \sqrt { 27 } } { 8 } ) \cdot 6 \sqrt { 3 }$$

Evaluate

$$12$$

Solution Steps

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$6\times \frac{-\frac{3}{4}}{-\frac{3\sqrt{3}}{8}}\sqrt{3}$$

Express \frac{-\frac{3}{4}}{-\frac{3\sqrt{3}}{8}} as a single fraction.

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

Cancel out 8, the greatest common factor in 4 and 8.

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

Divide -3 by \frac{3\sqrt{3}}{-2} by multiplying -3 by the reciprocal of \frac{3\sqrt{3}}{-2}.

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

Cancel out 3 in both numerator and denominator.

$$6\times \frac{-2\left(-1\right)}{\sqrt{3}}\sqrt{3}$$

Rationalize the denominator of \frac{-2\left(-1\right)}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$6\times \frac{-2\left(-1\right)\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\sqrt{3}$$

The square of \sqrt{3} is 3.

$$6\times \frac{-2\left(-1\right)\sqrt{3}}{3}\sqrt{3}$$

Multiply -2 and -1 to get 2.

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

Cancel out 3, the greatest common factor in 6 and 3.

$$2\times 2\sqrt{3}\sqrt{3}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{3}\sqrt{3}$$

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

$$4\times 3$$

Multiply 4 and 3 to get 12.

$$12$$

Factor

$$2^{2}\times 3$$