Solve sqrt{125*1/587.5}

$$\sqrt{ \frac{ 125 \cdot 1 }{ 587.5 } }$$

Evaluate

$$\frac{\sqrt{470}}{47}\approx 0.461265604$$

Solution Steps

Multiply 125 and 1 to get 125.

$$\sqrt{\frac{125}{587.5}}$$

Expand \frac{125}{587.5} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{1250}{5875}}$$

Reduce the fraction \frac{1250}{5875} to lowest terms by extracting and canceling out 125.

$$\sqrt{\frac{10}{47}}$$

Rewrite the square root of the division \sqrt{\frac{10}{47}} as the division of square roots \frac{\sqrt{10}}{\sqrt{47}}.

$$\frac{\sqrt{10}}{\sqrt{47}}$$

Rationalize the denominator of \frac{\sqrt{10}}{\sqrt{47}} by multiplying numerator and denominator by \sqrt{47}.

$$\frac{\sqrt{10}\sqrt{47}}{\left(\sqrt{47}\right)^{2}}$$

The square of \sqrt{47} is 47.

$$\frac{\sqrt{10}\sqrt{47}}{47}$$

To multiply \sqrt{10} and \sqrt{47}, multiply the numbers under the square root.

$$\frac{\sqrt{470}}{47}$$