Solve sqrt{566596*685div5122}

$$\sqrt{ 566596 \times 685 \div 5122 }$$

Evaluate

$$\frac{\sqrt{496985431930}}{2561}\approx 275.272134705$$

Solution Steps

Multiply 566596 and 685 to get 388118260.

$$\sqrt{\frac{388118260}{5122}}$$

Reduce the fraction \frac{388118260}{5122} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{194059130}{2561}}$$

Rewrite the square root of the division \sqrt{\frac{194059130}{2561}} as the division of square roots \frac{\sqrt{194059130}}{\sqrt{2561}}.

$$\frac{\sqrt{194059130}}{\sqrt{2561}}$$

Rationalize the denominator of \frac{\sqrt{194059130}}{\sqrt{2561}} by multiplying numerator and denominator by \sqrt{2561}.

$$\frac{\sqrt{194059130}\sqrt{2561}}{\left(\sqrt{2561}\right)^{2}}$$

The square of \sqrt{2561} is 2561.

$$\frac{\sqrt{194059130}\sqrt{2561}}{2561}$$

To multiply \sqrt{194059130} and \sqrt{2561}, multiply the numbers under the square root.

$$\frac{\sqrt{496985431930}}{2561}$$