Solve sqrt{200}-sqrt{8}-sqrt{50}

$$\sqrt { 200 } - \sqrt { 8 } - \sqrt { 50 }$$

Evaluate

$$3\sqrt{2}\approx 4.242640687$$

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}.

$$10\sqrt{2}-\sqrt{8}-\sqrt{50}$$

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}.

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

Combine 10\sqrt{2} and -2\sqrt{2} to get 8\sqrt{2}.

$$8\sqrt{2}-\sqrt{50}$$

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}.

$$8\sqrt{2}-5\sqrt{2}$$

Combine 8\sqrt{2} and -5\sqrt{2} to get 3\sqrt{2}.

$$3\sqrt{2}$$