Solve frac{6sqrt{2}}{frac{sqrt{2}}{2}}

$$\frac{ 6 \sqrt{ 2 } }{ \frac{ \sqrt{ 2 } }{ 2 } }$$

Evaluate

$$12$$

Solution Steps

Divide 6\sqrt{2} by \frac{\sqrt{2}}{2} by multiplying 6\sqrt{2} by the reciprocal of \frac{\sqrt{2}}{2}.

$$\frac{6\sqrt{2}\times 2}{\sqrt{2}}$$

Multiply 6 and 2 to get 12.

$$\frac{12\sqrt{2}}{\sqrt{2}}$$

Rationalize the denominator of \frac{12\sqrt{2}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{12\sqrt{2}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{12\sqrt{2}\sqrt{2}}{2}$$

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

$$\frac{12\times 2}{2}$$

Multiply 12 and 2 to get 24.

$$\frac{24}{2}$$

Divide 24 by 2 to get 12.

$$12$$

Factor

$$2^{2}\times 3$$