Solve frac{sqrt{50}-sqrt{18}}{sqrt{200}}

$$\frac { \sqrt { 50 } - \sqrt { 18 } } { \sqrt { 200 } }$$

Evaluate

$$\frac{1}{5}=0.2$$

Solution Steps

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}.

$$\frac{5\sqrt{2}-\sqrt{18}}{\sqrt{200}}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$\frac{5\sqrt{2}-3\sqrt{2}}{\sqrt{200}}$$

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

$$\frac{2\sqrt{2}}{\sqrt{200}}$$

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}.

$$\frac{2\sqrt{2}}{10\sqrt{2}}$$

Cancel out 2\sqrt{2} in both numerator and denominator.

$$\frac{1}{5}$$

Factor

$$\frac{1}{5} = 0.2$$