Solve =frac{sqrt{2}}{4sqrt{2}}*frac{sqrt{2}}{sqrt{2}}

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

Evaluate

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

Solution Steps

Divide \sqrt{2} by \sqrt{2} to get 1.

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

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

$$\frac{\sqrt{2}\sqrt{2}}{4\left(\sqrt{2}\right)^{2}}\times 1$$

The square of \sqrt{2} is 2.

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

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

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

Multiply 4 and 2 to get 8.

$$\frac{2}{8}\times 1$$

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

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

Multiply \frac{1}{4} and 1 to get \frac{1}{4}.

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

Factor

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