Solve sqrt{12}+sqrt{108}-sqrt{3}

$$\sqrt { 12 } + \sqrt { 108 } - \sqrt { 3 }$$

Evaluate

$$7\sqrt{3}\approx 12.124355653$$

Solution Steps

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}.

$$2\sqrt{3}+\sqrt{108}-\sqrt{3}$$

Factor 108=6^{2}\times 3. Rewrite the square root of the product \sqrt{6^{2}\times 3} as the product of square roots \sqrt{6^{2}}\sqrt{3}. Take the square root of 6^{2}.

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

Combine 2\sqrt{3} and 6\sqrt{3} to get 8\sqrt{3}.

$$8\sqrt{3}-\sqrt{3}$$

Combine 8\sqrt{3} and -\sqrt{3} to get 7\sqrt{3}.

$$7\sqrt{3}$$