Solve frac{sqrt{8}-sqrt{2}}{sqrt{50}}

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

Evaluate

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

Solution Steps

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}.

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

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

$$\frac{\sqrt{2}}{\sqrt{50}}$$

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}.

$$\frac{\sqrt{2}}{5\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{2}}{5\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{2}\sqrt{2}}{5\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{2}\sqrt{2}}{5\times 2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{2}{5\times 2}$$

Multiply 5 and 2 to get 10.

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

Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

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

Factor

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