Solve sqrt{8}+sqrt{12}+sqrt{8}

$$\sqrt { 8 } + \sqrt { 12 } + \sqrt { 8 }$$

Evaluate

$$2\left(\sqrt{3}+2\sqrt{2}\right)\approx 9.120955865$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$2\sqrt{2}+\sqrt{12}+\sqrt{8}$$

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}.

$$2\sqrt{2}+2\sqrt{3}+\sqrt{8}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

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

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

$$4\sqrt{2}+2\sqrt{3}$$