Solve sqrt{200}+sqrt{98}

$$\sqrt { 200 } + \sqrt { 98 }$$

Evaluate

$$17\sqrt{2}\approx 24.04163056$$

Solution Steps

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}.

$$10\sqrt{2}+\sqrt{98}$$

Factor 98=7^{2}\times 2. Rewrite the square root of the product \sqrt{7^{2}\times 2} as the product of square roots \sqrt{7^{2}}\sqrt{2}. Take the square root of 7^{2}.

$$10\sqrt{2}+7\sqrt{2}$$

Combine 10\sqrt{2} and 7\sqrt{2} to get 17\sqrt{2}.

$$17\sqrt{2}$$