Solve 1/2/-sqrt{2/4}=

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

Evaluate

$$-\sqrt{2}\approx -1.414213562$$

Solution Steps

Express \frac{\frac{1}{2}}{-\frac{\sqrt{2}}{4}} as a single fraction.

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

Cancel out 4, the greatest common factor in 2 and 4.

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

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

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

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

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

The square of \sqrt{2} is 2.

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

Cancel out 2 and 2.

$$-\sqrt{2}$$