Solve 6sqrt{5}*(-2/3*frac{sqrt{10}}{5})

$$6 \sqrt { 5 } \times ( - \frac { 2 } { 3 } \times \frac { \sqrt { 10 } } { 5 } )$$

Evaluate

$$-4\sqrt{2}\approx -5.656854249$$

Solution Steps

Express 6\left(-\frac{2}{3}\right) as a single fraction.

$$\frac{6\left(-2\right)}{3}\sqrt{5}\times \frac{\sqrt{10}}{5}$$

Multiply 6 and -2 to get -12.

$$\frac{-12}{3}\sqrt{5}\times \frac{\sqrt{10}}{5}$$

Divide -12 by 3 to get -4.

$$-4\sqrt{5}\times \frac{\sqrt{10}}{5}$$

Express -4\times \frac{\sqrt{10}}{5} as a single fraction.

$$\frac{-4\sqrt{10}}{5}\sqrt{5}$$

Express \frac{-4\sqrt{10}}{5}\sqrt{5} as a single fraction.

$$\frac{-4\sqrt{10}\sqrt{5}}{5}$$

Factor 10=5\times 2. Rewrite the square root of the product \sqrt{5\times 2} as the product of square roots \sqrt{5}\sqrt{2}.

$$\frac{-4\sqrt{5}\sqrt{2}\sqrt{5}}{5}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

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

Multiply -4 and 5 to get -20.

$$\frac{-20\sqrt{2}}{5}$$

Divide -20\sqrt{2} by 5 to get -4\sqrt{2}.

$$-4\sqrt{2}$$