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

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

Evaluate

$$\frac{1}{2}=0.5$$

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}.

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

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}.

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

Combine 5\sqrt{2} and -\sqrt{2} to get 4\sqrt{2}.

$$\frac{2\sqrt{2}}{4\sqrt{2}}$$

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

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$