Solve sqrt{500/851}

$$\sqrt { \frac { 500 } { 851 } }$$

Evaluate

$$\frac{10\sqrt{4255}}{851}\approx 0.766514231$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{500}{851}} as the division of square roots \frac{\sqrt{500}}{\sqrt{851}}.

$$\frac{\sqrt{500}}{\sqrt{851}}$$

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}.

$$\frac{10\sqrt{5}}{\sqrt{851}}$$

Rationalize the denominator of \frac{10\sqrt{5}}{\sqrt{851}} by multiplying numerator and denominator by \sqrt{851}.

$$\frac{10\sqrt{5}\sqrt{851}}{\left(\sqrt{851}\right)^{2}}$$

The square of \sqrt{851} is 851.

$$\frac{10\sqrt{5}\sqrt{851}}{851}$$

To multiply \sqrt{5} and \sqrt{851}, multiply the numbers under the square root.

$$\frac{10\sqrt{4255}}{851}$$