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

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

Evaluate

$$\sqrt{6}+2\sqrt{3}\approx 5.913591358$$

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}.

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

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

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

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

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