Solve sqrt{21/2}div3sqrt{28}*(-5sqrt{22/2})

$$\sqrt { 2 \frac { 1 } { 2 } } \div 3 \sqrt { 28 } \times ( - 5 \sqrt { 2 \frac { 2 } { 2 } } )$$

Evaluate

$$-\frac{5\sqrt{210}}{3}\approx -24.152294577$$

Solution Steps

Multiply 2 and 2 to get 4.

$$\frac{\sqrt{\frac{4+1}{2}}}{3}\sqrt{28}\left(-5\right)\sqrt{\frac{2\times 2+2}{2}}$$

Add 4 and 1 to get 5.

$$\frac{\sqrt{\frac{5}{2}}}{3}\sqrt{28}\left(-5\right)\sqrt{\frac{2\times 2+2}{2}}$$

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

$$\frac{\frac{\sqrt{5}}{\sqrt{2}}}{3}\sqrt{28}\left(-5\right)\sqrt{\frac{2\times 2+2}{2}}$$

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

$$\frac{\frac{\sqrt{5}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}}{3}\sqrt{28}\left(-5\right)\sqrt{\frac{2\times 2+2}{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\frac{\sqrt{5}\sqrt{2}}{2}}{3}\sqrt{28}\left(-5\right)\sqrt{\frac{2\times 2+2}{2}}$$

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

$$\frac{\frac{\sqrt{10}}{2}}{3}\sqrt{28}\left(-5\right)\sqrt{\frac{2\times 2+2}{2}}$$

Express \frac{\frac{\sqrt{10}}{2}}{3} as a single fraction.

$$\frac{\sqrt{10}}{2\times 3}\sqrt{28}\left(-5\right)\sqrt{\frac{2\times 2+2}{2}}$$

Multiply 2 and 3 to get 6.

$$\frac{\sqrt{10}}{6}\sqrt{28}\left(-5\right)\sqrt{\frac{2\times 2+2}{2}}$$

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

$$\frac{\sqrt{10}}{6}\times 2\sqrt{7}\left(-5\right)\sqrt{\frac{2\times 2+2}{2}}$$

Multiply 2 and -5 to get -10.

$$\frac{\sqrt{10}}{6}\left(-10\right)\sqrt{7}\sqrt{\frac{2\times 2+2}{2}}$$

Multiply 2 and 2 to get 4.

$$\frac{\sqrt{10}}{6}\left(-10\right)\sqrt{7}\sqrt{\frac{4+2}{2}}$$

Add 4 and 2 to get 6.

$$\frac{\sqrt{10}}{6}\left(-10\right)\sqrt{7}\sqrt{\frac{6}{2}}$$

Divide 6 by 2 to get 3.

$$\frac{\sqrt{10}}{6}\left(-10\right)\sqrt{7}\sqrt{3}$$

Express \frac{\sqrt{10}}{6}\left(-10\right) as a single fraction.

$$\frac{-\sqrt{10}\times 10}{6}\sqrt{7}\sqrt{3}$$

Express \frac{-\sqrt{10}\times 10}{6}\sqrt{7} as a single fraction.

$$\frac{-\sqrt{10}\times 10\sqrt{7}}{6}\sqrt{3}$$

Express \frac{-\sqrt{10}\times 10\sqrt{7}}{6}\sqrt{3} as a single fraction.

$$\frac{-\sqrt{10}\times 10\sqrt{7}\sqrt{3}}{6}$$

Multiply -1 and 10 to get -10.

$$\frac{-10\sqrt{10}\sqrt{7}\sqrt{3}}{6}$$

To multiply \sqrt{10} and \sqrt{7}, multiply the numbers under the square root.

$$\frac{-10\sqrt{70}\sqrt{3}}{6}$$

To multiply \sqrt{70} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{-10\sqrt{210}}{6}$$

Divide -10\sqrt{210} by 6 to get -\frac{5}{3}\sqrt{210}.

$$-\frac{5}{3}\sqrt{210}$$