Solve sqrt{24/5}*sqrt{4/3}*(-2sqrt{4/3})

$$\sqrt { \frac { 24 } { 5 } } \times \sqrt { \frac { 4 } { 3 } } \times ( - 2 \sqrt { \frac { 4 } { 3 } } )$$

Evaluate

$$-\frac{16\sqrt{30}}{15}\approx -5.842373947$$

Solution Steps

Multiply \sqrt{\frac{4}{3}} and \sqrt{\frac{4}{3}} to get \frac{4}{3}.

$$\sqrt{\frac{24}{5}}\times \frac{4}{3}\left(-2\right)$$

Rewrite the square root of the division \sqrt{\frac{24}{5}} as the division of square roots \frac{\sqrt{24}}{\sqrt{5}}.

$$\frac{\sqrt{24}}{\sqrt{5}}\times \frac{4}{3}\left(-2\right)$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$\frac{2\sqrt{6}}{\sqrt{5}}\times \frac{4}{3}\left(-2\right)$$

Rationalize the denominator of \frac{2\sqrt{6}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{2\sqrt{6}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\times \frac{4}{3}\left(-2\right)$$

The square of \sqrt{5} is 5.

$$\frac{2\sqrt{6}\sqrt{5}}{5}\times \frac{4}{3}\left(-2\right)$$

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

$$\frac{2\sqrt{30}}{5}\times \frac{4}{3}\left(-2\right)$$

Express \frac{4}{3}\left(-2\right) as a single fraction.

$$\frac{2\sqrt{30}}{5}\times \frac{4\left(-2\right)}{3}$$

Multiply 4 and -2 to get -8.

$$\frac{2\sqrt{30}}{5}\times \frac{-8}{3}$$

Fraction \frac{-8}{3} can be rewritten as -\frac{8}{3} by extracting the negative sign.

$$\frac{2\sqrt{30}}{5}\left(-\frac{8}{3}\right)$$

Multiply \frac{2\sqrt{30}}{5} times -\frac{8}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-2\sqrt{30}\times 8}{5\times 3}$$

Multiply -2 and 8 to get -16.

$$\frac{-16\sqrt{30}}{5\times 3}$$

Multiply 5 and 3 to get 15.

$$\frac{-16\sqrt{30}}{15}$$