Solve -3/4sqrt{8/3}*15*5/2

$$- \frac{ 3 }{ 4 } \sqrt{ \frac{ 8 }{ 3 } } \times 15 \times \frac{ 5 }{ 2 }$$

Evaluate

$$-\frac{75\sqrt{6}}{4}\approx -45.927932677$$

Solution Steps

Express 15\left(-\frac{3}{4}\right) as a single fraction.

$$\frac{15\left(-3\right)}{4}\sqrt{\frac{8}{3}}\times \frac{5}{2}$$

Multiply 15 and -3 to get -45.

$$\frac{-45}{4}\sqrt{\frac{8}{3}}\times \frac{5}{2}$$

Fraction \frac{-45}{4} can be rewritten as -\frac{45}{4} by extracting the negative sign.

$$-\frac{45}{4}\sqrt{\frac{8}{3}}\times \frac{5}{2}$$

Rewrite the square root of the division \sqrt{\frac{8}{3}} as the division of square roots \frac{\sqrt{8}}{\sqrt{3}}.

$$-\frac{45}{4}\times \frac{\sqrt{8}}{\sqrt{3}}\times \frac{5}{2}$$

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}.

$$-\frac{45}{4}\times \frac{2\sqrt{2}}{\sqrt{3}}\times \frac{5}{2}$$

Rationalize the denominator of \frac{2\sqrt{2}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$-\frac{45}{4}\times \frac{2\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\times \frac{5}{2}$$

The square of \sqrt{3} is 3.

$$-\frac{45}{4}\times \frac{2\sqrt{2}\sqrt{3}}{3}\times \frac{5}{2}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$-\frac{45}{4}\times \frac{2\sqrt{6}}{3}\times \frac{5}{2}$$

Multiply -\frac{45}{4} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-45\times 5}{4\times 2}\times \frac{2\sqrt{6}}{3}$$

Do the multiplications in the fraction \frac{-45\times 5}{4\times 2}.

$$\frac{-225}{8}\times \frac{2\sqrt{6}}{3}$$

Fraction \frac{-225}{8} can be rewritten as -\frac{225}{8} by extracting the negative sign.

$$-\frac{225}{8}\times \frac{2\sqrt{6}}{3}$$

Multiply -\frac{225}{8} times \frac{2\sqrt{6}}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-225\times 2\sqrt{6}}{8\times 3}$$

Cancel out 2\times 3 in both numerator and denominator.

$$\frac{-75\sqrt{6}}{4}$$