Solve frac{sqrt{500}}{sqrt{2012}}

$$\frac { \sqrt { 500 } } { \sqrt { 2012 } }$$

Evaluate

$$\frac{5\sqrt{2515}}{503}\approx 0.498506716$$

Solution Steps

Factor 500=10^{2}\times 5. Rewrite the square root of the product \sqrt{10^{2}\times 5} as the product of square roots \sqrt{10^{2}}\sqrt{5}. Take the square root of 10^{2}.

$$\frac{10\sqrt{5}}{\sqrt{2012}}$$

Factor 2012=2^{2}\times 503. Rewrite the square root of the product \sqrt{2^{2}\times 503} as the product of square roots \sqrt{2^{2}}\sqrt{503}. Take the square root of 2^{2}.

$$\frac{10\sqrt{5}}{2\sqrt{503}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{5\sqrt{5}}{\sqrt{503}}$$

Rationalize the denominator of \frac{5\sqrt{5}}{\sqrt{503}} by multiplying numerator and denominator by \sqrt{503}.

$$\frac{5\sqrt{5}\sqrt{503}}{\left(\sqrt{503}\right)^{2}}$$

The square of \sqrt{503} is 503.

$$\frac{5\sqrt{5}\sqrt{503}}{503}$$

To multiply \sqrt{5} and \sqrt{503}, multiply the numbers under the square root.

$$\frac{5\sqrt{2515}}{503}$$