Solve 36sqrt{5}*(-1/4)sqrt{8/3}=

$$36 \sqrt{ 5 } \times (- \frac{ 1 }{ 4 } ) \sqrt{ \frac{ 8 }{ 3 } } =$$

Evaluate

$$-6\sqrt{30}\approx -32.86335345$$

Solution Steps

Express 36\left(-\frac{1}{4}\right) as a single fraction.

$$\frac{36\left(-1\right)}{4}\sqrt{5}\sqrt{\frac{8}{3}}$$

Multiply 36 and -1 to get -36.

$$\frac{-36}{4}\sqrt{5}\sqrt{\frac{8}{3}}$$

Divide -36 by 4 to get -9.

$$-9\sqrt{5}\sqrt{\frac{8}{3}}$$

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

$$-9\sqrt{5}\times \frac{\sqrt{8}}{\sqrt{3}}$$

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}.

$$-9\sqrt{5}\times \frac{2\sqrt{2}}{\sqrt{3}}$$

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

$$-9\sqrt{5}\times \frac{2\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$-9\sqrt{5}\times \frac{2\sqrt{2}\sqrt{3}}{3}$$

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

$$-9\sqrt{5}\times \frac{2\sqrt{6}}{3}$$

Cancel out 3, the greatest common factor in 9 and 3.

$$-3\times 2\sqrt{6}\sqrt{5}$$

Multiply -3 and 2 to get -6.

$$-6\sqrt{6}\sqrt{5}$$

To multiply \sqrt{6} and \sqrt{5}, multiply the numbers under the square root.

$$-6\sqrt{30}$$