Solve sqrt{24}-sqrt{54}

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

Evaluate

$$-\sqrt{6}\approx -2.449489743$$

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}.

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

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}.

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

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

$$-\sqrt{6}$$