Solve -2sqrt{24}-3sqrt{54}

$$- 2 \sqrt { 24 } - 3 \sqrt { 54 }$$

Evaluate

$$-13\sqrt{6}\approx -31.843366656$$

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}.

$$-2\times 2\sqrt{6}-3\sqrt{54}$$

Multiply -2 and 2 to get -4.

$$-4\sqrt{6}-3\sqrt{54}$$

Factor 54=3^{2}\times 6. Rewrite the square root of the product \sqrt{3^{2}\times 6} as the product of square roots \sqrt{3^{2}}\sqrt{6}. Take the square root of 3^{2}.

$$-4\sqrt{6}-3\times 3\sqrt{6}$$

Multiply -3 and 3 to get -9.

$$-4\sqrt{6}-9\sqrt{6}$$

Combine -4\sqrt{6} and -9\sqrt{6} to get -13\sqrt{6}.

$$-13\sqrt{6}$$