Solve frac{sqrt{2}}{sqrt{32}}

$$\frac { \sqrt { 2 } } { \sqrt { 32 } }$$

Evaluate

$$\frac{1}{4}=0.25$$

Solution Steps

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

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

Rationalize the denominator of \frac{\sqrt{2}}{4\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{2}\sqrt{2}}{4\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

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

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

$$\frac{2}{4\times 2}$$

Multiply 4 and 2 to get 8.

$$\frac{2}{8}$$

Reduce the fraction \frac{2}{8} to lowest terms by extracting and canceling out 2.

$$\frac{1}{4}$$

Factor

$$\frac{1}{2 ^ {2}} = 0.25$$