Solve sqrt{54}-sqrt{24}-sqrt{6}+12=

$$\sqrt{ 54 } - \sqrt{ 24 } - \sqrt{ 6 } +12=$$

Evaluate

$$12$$

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}.

$$3\sqrt{6}-\sqrt{24}-\sqrt{6}+12$$

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}.

$$3\sqrt{6}-2\sqrt{6}-\sqrt{6}+12$$

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

$$\sqrt{6}-\sqrt{6}+12$$

Combine \sqrt{6} and -\sqrt{6} to get 0.

$$12$$

Factor

$$2^{2}\times 3$$