Solve sqrt{16}+sqrt{50}-sqrt{200}

$$\sqrt { 16 } + \sqrt { 50 } - \sqrt { 200 }$$

Evaluate

$$4-5\sqrt{2}\approx -3.071067812$$

Solution Steps

Calculate the square root of 16 and get 4.

$$4+\sqrt{50}-\sqrt{200}$$

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}.

$$4+5\sqrt{2}-\sqrt{200}$$

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}.

$$4+5\sqrt{2}-10\sqrt{2}$$

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

$$4-5\sqrt{2}$$