Solve 400/sqrt{2}div10

$$\frac{ 400 }{ \sqrt{ 2 } } \div 10$$

Evaluate

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

Solution Steps

Express \frac{\frac{400}{\sqrt{2}}}{10} as a single fraction.

$$\frac{400}{\sqrt{2}\times 10}$$

Rationalize the denominator of \frac{400}{\sqrt{2}\times 10} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{400\sqrt{2}}{\left(\sqrt{2}\right)^{2}\times 10}$$

The square of \sqrt{2} is 2.

$$\frac{400\sqrt{2}}{2\times 10}$$

Cancel out 2\times 10 in both numerator and denominator.

$$20\sqrt{2}$$