Solve sqrt{8}+sqrt{18}+sqrt{24}

$$\sqrt { 8 } + \sqrt { 18 } + \sqrt { 24 }$$

Evaluate

$$\sqrt{2}\left(2\sqrt{3}+5\right)\approx 11.970047297$$

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}.

$$2\sqrt{2}+\sqrt{18}+\sqrt{24}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$2\sqrt{2}+3\sqrt{2}+\sqrt{24}$$

Combine 2\sqrt{2} and 3\sqrt{2} to get 5\sqrt{2}.

$$5\sqrt{2}+\sqrt{24}$$

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}.

$$5\sqrt{2}+2\sqrt{6}$$