Solve (-5sqrt{24})*(-4sqrt{80})

$$( - 5 \sqrt { 24 } ) \times ( - 4 \sqrt { 80 } )$$

Evaluate

$$160\sqrt{30}\approx 876.356092008$$

Solution Steps

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}.

$$-5\times 2\sqrt{6}\left(-4\right)\sqrt{80}$$

Multiply -5 and 2 to get -10.

$$-10\sqrt{6}\left(-4\right)\sqrt{80}$$

Multiply -10 and -4 to get 40.

$$40\sqrt{6}\sqrt{80}$$

Factor 80=4^{2}\times 5. Rewrite the square root of the product \sqrt{4^{2}\times 5} as the product of square roots \sqrt{4^{2}}\sqrt{5}. Take the square root of 4^{2}.

$$40\sqrt{6}\times 4\sqrt{5}$$

Multiply 40 and 4 to get 160.

$$160\sqrt{6}\sqrt{5}$$

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

$$160\sqrt{30}$$