Solve (-3/4):(-frac{sqrt{23}}{8})*6sqrt{3}

$$( - \frac { 3 } { 4 } ) : ( - \frac { \sqrt { 23 } } { 8 } ) \cdot 6 \sqrt { 3 }$$

Evaluate

$$\frac{36\sqrt{69}}{23}\approx 13.001672133$$

Solution Steps

Express \frac{-\frac{3}{4}}{-\frac{\sqrt{23}}{8}} as a single fraction.

$$6\times \frac{-3}{4\left(-\frac{\sqrt{23}}{8}\right)}\sqrt{3}$$

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

$$6\times \frac{-3}{\frac{\sqrt{23}}{-2}}\sqrt{3}$$

Divide -3 by \frac{\sqrt{23}}{-2} by multiplying -3 by the reciprocal of \frac{\sqrt{23}}{-2}.

$$6\times \frac{-3\left(-2\right)}{\sqrt{23}}\sqrt{3}$$

Rationalize the denominator of \frac{-3\left(-2\right)}{\sqrt{23}} by multiplying numerator and denominator by \sqrt{23}.

$$6\times \frac{-3\left(-2\right)\sqrt{23}}{\left(\sqrt{23}\right)^{2}}\sqrt{3}$$

The square of \sqrt{23} is 23.

$$6\times \frac{-3\left(-2\right)\sqrt{23}}{23}\sqrt{3}$$

Multiply -3 and -2 to get 6.

$$6\times \frac{6\sqrt{23}}{23}\sqrt{3}$$

Express 6\times \frac{6\sqrt{23}}{23} as a single fraction.

$$\frac{6\times 6\sqrt{23}}{23}\sqrt{3}$$

Express \frac{6\times 6\sqrt{23}}{23}\sqrt{3} as a single fraction.

$$\frac{6\times 6\sqrt{23}\sqrt{3}}{23}$$

Multiply 6 and 6 to get 36.

$$\frac{36\sqrt{23}\sqrt{3}}{23}$$

To multiply \sqrt{23} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{36\sqrt{69}}{23}$$