Solve 6sqrt{75}*(-3/2*sqrt{3}3/4)div(-9sqrt{20})

$$6 \sqrt { 75 } \times ( - \frac { 3 } { 2 } \times \sqrt { 3 } \frac { 3 } { 4 } ) \div ( - 9 \sqrt { 20 } )$$

Evaluate

$$\frac{9\sqrt{5}}{8}\approx 2.515576475$$

Solution Steps

Cancel out 3 in both numerator and denominator.

$$\frac{-\frac{3}{2}\times \frac{3}{4}\times 2\sqrt{3}\sqrt{75}}{-3\sqrt{20}}$$

Factor 75=3\times 25. Rewrite the square root of the product \sqrt{3\times 25} as the product of square roots \sqrt{3}\sqrt{25}.

$$\frac{-\frac{3}{2}\times \frac{3}{4}\times 2\sqrt{3}\sqrt{3}\sqrt{25}}{-3\sqrt{20}}$$

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

$$\frac{-\frac{3}{2}\times \frac{3}{4}\times 2\times 3\sqrt{25}}{-3\sqrt{20}}$$

Multiply -\frac{3}{2} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-3\times 3}{2\times 4}\times 2\times 3\sqrt{25}}{-3\sqrt{20}}$$

Do the multiplications in the fraction \frac{-3\times 3}{2\times 4}.

$$\frac{\frac{-9}{8}\times 2\times 3\sqrt{25}}{-3\sqrt{20}}$$

Fraction \frac{-9}{8} can be rewritten as -\frac{9}{8} by extracting the negative sign.

$$\frac{-\frac{9}{8}\times 2\times 3\sqrt{25}}{-3\sqrt{20}}$$

Express -\frac{9}{8}\times 2 as a single fraction.

$$\frac{\frac{-9\times 2}{8}\times 3\sqrt{25}}{-3\sqrt{20}}$$

Multiply -9 and 2 to get -18.

$$\frac{\frac{-18}{8}\times 3\sqrt{25}}{-3\sqrt{20}}$$

Reduce the fraction \frac{-18}{8} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{9}{4}\times 3\sqrt{25}}{-3\sqrt{20}}$$

Express -\frac{9}{4}\times 3 as a single fraction.

$$\frac{\frac{-9\times 3}{4}\sqrt{25}}{-3\sqrt{20}}$$

Multiply -9 and 3 to get -27.

$$\frac{\frac{-27}{4}\sqrt{25}}{-3\sqrt{20}}$$

Fraction \frac{-27}{4} can be rewritten as -\frac{27}{4} by extracting the negative sign.

$$\frac{-\frac{27}{4}\sqrt{25}}{-3\sqrt{20}}$$

Calculate the square root of 25 and get 5.

$$\frac{-\frac{27}{4}\times 5}{-3\sqrt{20}}$$

Express -\frac{27}{4}\times 5 as a single fraction.

$$\frac{\frac{-27\times 5}{4}}{-3\sqrt{20}}$$

Multiply -27 and 5 to get -135.

$$\frac{\frac{-135}{4}}{-3\sqrt{20}}$$

Fraction \frac{-135}{4} can be rewritten as -\frac{135}{4} by extracting the negative sign.

$$\frac{-\frac{135}{4}}{-3\sqrt{20}}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$\frac{-\frac{135}{4}}{-3\times 2\sqrt{5}}$$

Multiply -3 and 2 to get -6.

$$\frac{-\frac{135}{4}}{-6\sqrt{5}}$$

Express \frac{-\frac{135}{4}}{-6\sqrt{5}} as a single fraction.

$$\frac{-135}{4\left(-6\right)\sqrt{5}}$$

Rationalize the denominator of \frac{-135}{4\left(-6\right)\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{-135\sqrt{5}}{4\left(-6\right)\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{-135\sqrt{5}}{4\left(-6\right)\times 5}$$

Cancel out 3\times 5 in both numerator and denominator.

$$\frac{-9\sqrt{5}}{-2\times 4}$$

Multiply -2 and 4 to get -8.

$$\frac{-9\sqrt{5}}{-8}$$