Solve 5/sqrt{2}*frac{sqrt{2}}{2}

$$\frac { 5 } { \sqrt { 2 } } \cdot \frac { \sqrt { 2 } } { 2 }$$

Evaluate

$$\frac{5}{2}=2.5$$

Solution Steps

Rationalize the denominator of \frac{5}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{5\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\times \frac{\sqrt{2}}{2}$$

The square of \sqrt{2} is 2.

$$\frac{5\sqrt{2}}{2}\times \frac{\sqrt{2}}{2}$$

Multiply \frac{5\sqrt{2}}{2} times \frac{\sqrt{2}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\sqrt{2}\sqrt{2}}{2\times 2}$$

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

$$\frac{5\times 2}{2\times 2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{5}{2}$$

Factor

$$\frac{5}{2} = 2\frac{1}{2} = 2.5$$