Solve 3sqrt{22/3}div2sqrt{2/5}*(-1/8sqrt{15})

$$3 \sqrt { 2 \frac { 2 } { 3 } } \div 2 \sqrt { \frac { 2 } { 5 } } \times ( - \frac { 1 } { 8 } \sqrt { 15 } )$$

Evaluate

$$-\frac{3}{4}=-0.75$$

Solution Steps

Multiply 2 and 3 to get 6.

$$\frac{3\sqrt{\frac{6+2}{3}}}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

Add 6 and 2 to get 8.

$$\frac{3\sqrt{\frac{8}{3}}}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

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

$$\frac{3\times \frac{\sqrt{8}}{\sqrt{3}}}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

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}.

$$\frac{3\times \frac{2\sqrt{2}}{\sqrt{3}}}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

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

$$\frac{3\times \frac{2\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

The square of \sqrt{3} is 3.

$$\frac{3\times \frac{2\sqrt{2}\sqrt{3}}{3}}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

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

$$\frac{3\times \frac{2\sqrt{6}}{3}}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

Cancel out 3 and 3.

$$\frac{2\sqrt{6}}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

Cancel out 2 and 2.

$$\sqrt{6}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

Rewrite the square root of the division \sqrt{\frac{2}{5}} as the division of square roots \frac{\sqrt{2}}{\sqrt{5}}.

$$\sqrt{6}\times \frac{\sqrt{2}}{\sqrt{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

Rationalize the denominator of \frac{\sqrt{2}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\sqrt{6}\times \frac{\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\left(-\frac{1}{8}\right)\sqrt{15}$$

The square of \sqrt{5} is 5.

$$\sqrt{6}\times \frac{\sqrt{2}\sqrt{5}}{5}\left(-\frac{1}{8}\right)\sqrt{15}$$

To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.

$$\sqrt{6}\times \frac{\sqrt{10}}{5}\left(-\frac{1}{8}\right)\sqrt{15}$$

Express \sqrt{6}\times \frac{\sqrt{10}}{5} as a single fraction.

$$\frac{\sqrt{6}\sqrt{10}}{5}\left(-\frac{1}{8}\right)\sqrt{15}$$

Multiply \frac{\sqrt{6}\sqrt{10}}{5} times -\frac{1}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\sqrt{6}\sqrt{10}}{5\times 8}\sqrt{15}$$

Express \frac{-\sqrt{6}\sqrt{10}}{5\times 8}\sqrt{15} as a single fraction.

$$\frac{-\sqrt{6}\sqrt{10}\sqrt{15}}{5\times 8}$$

To multiply \sqrt{6} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{-\sqrt{60}\sqrt{15}}{5\times 8}$$

Factor 60=15\times 4. Rewrite the square root of the product \sqrt{15\times 4} as the product of square roots \sqrt{15}\sqrt{4}.

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

Multiply \sqrt{15} and \sqrt{15} to get 15.

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

Multiply 5 and 8 to get 40.

$$\frac{-15\sqrt{4}}{40}$$

Calculate the square root of 4 and get 2.

$$\frac{-15\times 2}{40}$$

Multiply -15 and 2 to get -30.

$$\frac{-30}{40}$$

Reduce the fraction \frac{-30}{40} to lowest terms by extracting and canceling out 10.

$$-\frac{3}{4}$$

Factor

$$-\frac{3}{4} = -0.75$$