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

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

Evaluate

$$-\frac{10\sqrt{35}}{3}\approx -19.720265944$$

Solution Steps

Factor 28=2\times 14. Rewrite the square root of the product \sqrt{2\times 14} as the product of square roots \sqrt{2}\sqrt{14}.

$$\frac{\sqrt{\frac{5}{2}}}{3}\sqrt{2}\sqrt{14}\left(-5\right)\sqrt{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{\sqrt{\frac{5}{2}}}{3}\times 2\left(-5\right)\sqrt{14}$$

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

$$\frac{\frac{\sqrt{5}}{\sqrt{2}}}{3}\times 2\left(-5\right)\sqrt{14}$$

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

$$\frac{\frac{\sqrt{5}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}}{3}\times 2\left(-5\right)\sqrt{14}$$

The square of \sqrt{2} is 2.

$$\frac{\frac{\sqrt{5}\sqrt{2}}{2}}{3}\times 2\left(-5\right)\sqrt{14}$$

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

$$\frac{\frac{\sqrt{10}}{2}}{3}\times 2\left(-5\right)\sqrt{14}$$

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

$$\frac{\sqrt{10}}{2\times 3}\times 2\left(-5\right)\sqrt{14}$$

Multiply 2 and 3 to get 6.

$$\frac{\sqrt{10}}{6}\times 2\left(-5\right)\sqrt{14}$$

Multiply 2 and -5 to get -10.

$$\frac{\sqrt{10}}{6}\left(-10\right)\sqrt{14}$$

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

$$\frac{-\sqrt{10}\times 10}{6}\sqrt{14}$$

Express \frac{-\sqrt{10}\times 10}{6}\sqrt{14} as a single fraction.

$$\frac{-\sqrt{10}\times 10\sqrt{14}}{6}$$

Multiply -1 and 10 to get -10.

$$\frac{-10\sqrt{10}\sqrt{14}}{6}$$

To multiply \sqrt{10} and \sqrt{14}, multiply the numbers under the square root.

$$\frac{-10\sqrt{140}}{6}$$

Factor 140=2^{2}\times 35. Rewrite the square root of the product \sqrt{2^{2}\times 35} as the product of square roots \sqrt{2^{2}}\sqrt{35}. Take the square root of 2^{2}.

$$\frac{-10\times 2\sqrt{35}}{6}$$

Multiply -10 and 2 to get -20.

$$\frac{-20\sqrt{35}}{6}$$

Divide -20\sqrt{35} by 6 to get -\frac{10}{3}\sqrt{35}.

$$-\frac{10}{3}\sqrt{35}$$