Solve sqrt{2/16}

$$\sqrt { \frac { 2 } { 16 } }$$

Evaluate

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

Solution Steps

Reduce the fraction \frac{2}{16} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{1}{8}}$$

Rewrite the square root of the division \sqrt{\frac{1}{8}} as the division of square roots \frac{\sqrt{1}}{\sqrt{8}}.

$$\frac{\sqrt{1}}{\sqrt{8}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{8}}$$

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}.

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

Rationalize the denominator of \frac{1}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

Multiply 2 and 2 to get 4.

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