Solve frac{-2sqrt{2}}{-frac{sqrt{2}}{2}}=

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

Evaluate

$$4$$

Solution Steps

Cancel out -1 in both numerator and denominator.

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

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

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

Multiply 2 and 2 to get 4.

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

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

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

The square of \sqrt{2} is 2.

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

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

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

Multiply 4 and 2 to get 8.

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

Divide 8 by 2 to get 4.

$$4$$

Factor

$$2^{2}$$