Solve sqrt{50}+sqrt{352}+5sqrt{2}

$$\sqrt { 50 } + \sqrt { 352 } + 5 \sqrt { 2 }$$

Evaluate

$$2\sqrt{2}\left(2\sqrt{11}+5\right)\approx 32.903798663$$

Solution Steps

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$5\sqrt{2}+\sqrt{352}+5\sqrt{2}$$

Factor 352=4^{2}\times 22. Rewrite the square root of the product \sqrt{4^{2}\times 22} as the product of square roots \sqrt{4^{2}}\sqrt{22}. Take the square root of 4^{2}.

$$5\sqrt{2}+4\sqrt{22}+5\sqrt{2}$$

Combine 5\sqrt{2} and 5\sqrt{2} to get 10\sqrt{2}.

$$10\sqrt{2}+4\sqrt{22}$$