Solve sqrt{54}+sqrt{150}-sqrt{24}

$$\sqrt { 54 } + \sqrt { 150 } - \sqrt { 24 }$$

Evaluate

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

Solution Steps

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}.

$$3\sqrt{6}+\sqrt{150}-\sqrt{24}$$

Factor 150=5^{2}\times 6. Rewrite the square root of the product \sqrt{5^{2}\times 6} as the product of square roots \sqrt{5^{2}}\sqrt{6}. Take the square root of 5^{2}.

$$3\sqrt{6}+5\sqrt{6}-\sqrt{24}$$

Combine 3\sqrt{6} and 5\sqrt{6} to get 8\sqrt{6}.

$$8\sqrt{6}-\sqrt{24}$$

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}.

$$8\sqrt{6}-2\sqrt{6}$$

Combine 8\sqrt{6} and -2\sqrt{6} to get 6\sqrt{6}.

$$6\sqrt{6}$$