Solve sqrt{800}+sqrt{200}

$$\sqrt{ 800 } + \sqrt{ 200 }$$

Evaluate

$$30\sqrt{2}\approx 42.426406871$$

Solution Steps

Factor 800=20^{2}\times 2. Rewrite the square root of the product \sqrt{20^{2}\times 2} as the product of square roots \sqrt{20^{2}}\sqrt{2}. Take the square root of 20^{2}.

$$20\sqrt{2}+\sqrt{200}$$

Factor 200=10^{2}\times 2. Rewrite the square root of the product \sqrt{10^{2}\times 2} as the product of square roots \sqrt{10^{2}}\sqrt{2}. Take the square root of 10^{2}.

$$20\sqrt{2}+10\sqrt{2}$$

Combine 20\sqrt{2} and 10\sqrt{2} to get 30\sqrt{2}.

$$30\sqrt{2}$$