Solve sqrt{200}-sqrt{50}

$$\sqrt { 200 } - \sqrt { 50 }$$

Evaluate

$$5\sqrt{2}\approx 7.071067812$$

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}.

$$10\sqrt{2}-\sqrt{50}$$

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}.

$$10\sqrt{2}-5\sqrt{2}$$

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

$$5\sqrt{2}$$