Solve sqrt{44}+sqrt{12}+2sqrt{6}

$$\sqrt { 44 } + \sqrt { 12 } + 2 \sqrt { 6 }$$

Evaluate

$$2\left(\sqrt{3}+\sqrt{6}+\sqrt{11}\right)\approx 14.996330681$$

Solution Steps

Factor 44=2^{2}\times 11. Rewrite the square root of the product \sqrt{2^{2}\times 11} as the product of square roots \sqrt{2^{2}}\sqrt{11}. Take the square root of 2^{2}.

$$2\sqrt{11}+\sqrt{12}+2\sqrt{6}$$

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}.

$$2\sqrt{11}+2\sqrt{3}+2\sqrt{6}$$