Solve sqrt{96}-sqrt{24}-3sqrt{54}=

$$\sqrt { 96 } - \sqrt { 24 } - 3 \sqrt { 54 } =$$

Evaluate

$$-7\sqrt{6}\approx -17.146428199$$

Solution Steps

Factor 96=4^{2}\times 6. Rewrite the square root of the product \sqrt{4^{2}\times 6} as the product of square roots \sqrt{4^{2}}\sqrt{6}. Take the square root of 4^{2}.

$$4\sqrt{6}-\sqrt{24}-3\sqrt{54}$$

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}.

$$4\sqrt{6}-2\sqrt{6}-3\sqrt{54}$$

Combine 4\sqrt{6} and -2\sqrt{6} to get 2\sqrt{6}.

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

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}.

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

Multiply -3 and 3 to get -9.

$$2\sqrt{6}-9\sqrt{6}$$

Combine 2\sqrt{6} and -9\sqrt{6} to get -7\sqrt{6}.

$$-7\sqrt{6}$$