Solve 4sqrt{6}-sqrt{24}+sqrt{54}

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

Evaluate

$$5\sqrt{6}\approx 12.247448714$$

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}.

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

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

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

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 5\sqrt{6}.

$$5\sqrt{6}$$