Solve frac{sqrt{1.000}}{sqrt{250}}

$$\frac { \sqrt { 1.000 } } { \sqrt { 250 } }$$

Evaluate

$$\frac{\sqrt{10}}{50}\approx 0.063245553$$

Solution Steps

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{250}}$$

Factor 250=5^{2}\times 10. Rewrite the square root of the product \sqrt{5^{2}\times 10} as the product of square roots \sqrt{5^{2}}\sqrt{10}. Take the square root of 5^{2}.

$$\frac{1}{5\sqrt{10}}$$

Rationalize the denominator of \frac{1}{5\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{\sqrt{10}}{5\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{\sqrt{10}}{5\times 10}$$

Multiply 5 and 10 to get 50.

$$\frac{\sqrt{10}}{50}$$