Solve sqrt{2}-sqrt{200}+sqrt{75}

$$\sqrt { 2 } - \sqrt { 200 } + \sqrt { 75 }$$

Evaluate

$$5\sqrt{3}-9\sqrt{2}\approx -4.067668024$$

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}.

$$\sqrt{2}-10\sqrt{2}+\sqrt{75}$$

Combine \sqrt{2} and -10\sqrt{2} to get -9\sqrt{2}.

$$-9\sqrt{2}+\sqrt{75}$$

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$-9\sqrt{2}+5\sqrt{3}$$