Solve sqrt{625/3,14}

$$\sqrt { \frac { 625 } { 3,14 } }$$

Evaluate

$$\frac{125\sqrt{314}}{157}\approx 14.1083162$$

Solution Steps

Expand \frac{625}{3,14} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{62500}{314}}$$

Reduce the fraction \frac{62500}{314} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{31250}{157}}$$

Rewrite the square root of the division \sqrt{\frac{31250}{157}} as the division of square roots \frac{\sqrt{31250}}{\sqrt{157}}.

$$\frac{\sqrt{31250}}{\sqrt{157}}$$

Factor 31250=125^{2}\times 2. Rewrite the square root of the product \sqrt{125^{2}\times 2} as the product of square roots \sqrt{125^{2}}\sqrt{2}. Take the square root of 125^{2}.

$$\frac{125\sqrt{2}}{\sqrt{157}}$$

Rationalize the denominator of \frac{125\sqrt{2}}{\sqrt{157}} by multiplying numerator and denominator by \sqrt{157}.

$$\frac{125\sqrt{2}\sqrt{157}}{\left(\sqrt{157}\right)^{2}}$$

The square of \sqrt{157} is 157.

$$\frac{125\sqrt{2}\sqrt{157}}{157}$$

To multiply \sqrt{2} and \sqrt{157}, multiply the numbers under the square root.

$$\frac{125\sqrt{314}}{157}$$