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

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

Evaluate

$$\frac{\sqrt{2}}{4}\approx 0.353553391$$

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}.

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

Divide 2\sqrt{2} by 8 to get \frac{1}{4}\sqrt{2}.

$$\frac{\sqrt{2}}{2}-\frac{1}{4}\sqrt{2}$$

Combine \frac{\sqrt{2}}{2} and -\frac{1}{4}\sqrt{2} to get \frac{1}{4}\sqrt{2}.

$$\frac{1}{4}\sqrt{2}$$