Solve 1/2sqrt{2}*1/frac{1{4}sqrt{2}}

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

Evaluate

$$2$$

Solution Steps

Rationalize the denominator of \frac{1}{\frac{1}{4}\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

Multiply \frac{1}{4} and 2 to get \frac{2}{4}.

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

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

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

Divide \sqrt{2} by \frac{1}{2} by multiplying \sqrt{2} by the reciprocal of \frac{1}{2}.

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

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

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

Cancel out 2 and 2.

$$2$$

Factor

$$2$$