Solve sqrt{200/400}

$$\sqrt{ \frac{ 200 }{ 400 } }$$

Evaluate

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

Solution Steps

Reduce the fraction \frac{200}{400} to lowest terms by extracting and canceling out 200.

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

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

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

Calculate the square root of 1 and get 1.

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

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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