Solve sqrt{24}-sqrt{54}+sqrt{96}

$$\sqrt { 24 } - \sqrt { 54 } + \sqrt { 96 }$$

Evaluate

$$3\sqrt{6}\approx 7.348469228$$

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}.

$$2\sqrt{6}-\sqrt{54}+\sqrt{96}$$

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}.

$$2\sqrt{6}-3\sqrt{6}+\sqrt{96}$$

Combine 2\sqrt{6} and -3\sqrt{6} to get -\sqrt{6}.

$$-\sqrt{6}+\sqrt{96}$$

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}.

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

Combine -\sqrt{6} and 4\sqrt{6} to get 3\sqrt{6}.

$$3\sqrt{6}$$