Solve 100divfrac{5sqrt{2}}{2}

$$100 \div \frac { 5 \sqrt { 2 } } { 2 }$$

Evaluate

$$20\sqrt{2}\approx 28.284271247$$

Solution Steps

Divide 100 by \frac{5\sqrt{2}}{2} by multiplying 100 by the reciprocal of \frac{5\sqrt{2}}{2}.

$$\frac{100\times 2}{5\sqrt{2}}$$

Cancel out 5 in both numerator and denominator.

$$\frac{2\times 20}{\sqrt{2}}$$

Multiply 2 and 20 to get 40.

$$\frac{40}{\sqrt{2}}$$

Rationalize the denominator of \frac{40}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{40\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{40\sqrt{2}}{2}$$

Divide 40\sqrt{2} by 2 to get 20\sqrt{2}.

$$20\sqrt{2}$$