Solve sqrt{24}-5sqrt{6}+sqrt{486}

$$\sqrt { 24 } - 5 \sqrt { 6 } + \sqrt { 486 }$$

Evaluate

$$6\sqrt{6}\approx 14.696938457$$

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}.

$$2\sqrt{6}-5\sqrt{6}+\sqrt{486}$$

Combine 2\sqrt{6} and -5\sqrt{6} to get -3\sqrt{6}.

$$-3\sqrt{6}+\sqrt{486}$$

Factor 486=9^{2}\times 6. Rewrite the square root of the product \sqrt{9^{2}\times 6} as the product of square roots \sqrt{9^{2}}\sqrt{6}. Take the square root of 9^{2}.

$$-3\sqrt{6}+9\sqrt{6}$$

Combine -3\sqrt{6} and 9\sqrt{6} to get 6\sqrt{6}.

$$6\sqrt{6}$$