Solve 4sqrt{2/4}:2/4

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

Evaluate

$$4\sqrt{2}\approx 5.656854249$$

Solution Steps

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

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

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{2} is 2.

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

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

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

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

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

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

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

Multiply 2 and 2 to get 4.

$$4\sqrt{2}$$