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

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

Evaluate

$$\frac{\sqrt{2}}{2}\approx 0.707106781$$

Solution Steps

Divide \sqrt{2} by \sqrt{2} to get 1.

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

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

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

The square of \sqrt{2} is 2.

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

Cancel out 4 in both numerator and denominator.

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

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

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