Solve 5/80*sqrt{2}*9=

$$\frac{ 5 }{ 80 \times \sqrt{ 2 } } \times 9=$$

Evaluate

$$\frac{9\sqrt{2}}{32}\approx 0.397747564$$

Solution Steps

Rationalize the denominator of \frac{5}{80\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$9\times \frac{5\sqrt{2}}{80\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$9\times \frac{5\sqrt{2}}{80\times 2}$$

Cancel out 5 in both numerator and denominator.

$$9\times \frac{\sqrt{2}}{2\times 16}$$

Multiply 2 and 16 to get 32.

$$9\times \frac{\sqrt{2}}{32}$$

Express 9\times \frac{\sqrt{2}}{32} as a single fraction.

$$\frac{9\sqrt{2}}{32}$$