Evaluate
\frac{19\sqrt{70189}}{10027}\approx 0.502015485
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\sqrt{\frac{10108}{40108}}
Expand \frac{101.08}{401.08} by multiplying both numerator and the denominator by 100.
\sqrt{\frac{2527}{10027}}
Reduce the fraction \frac{10108}{40108} to lowest terms by extracting and canceling out 4.
\frac{\sqrt{2527}}{\sqrt{10027}}
Rewrite the square root of the division \sqrt{\frac{2527}{10027}} as the division of square roots \frac{\sqrt{2527}}{\sqrt{10027}}.
\frac{19\sqrt{7}}{\sqrt{10027}}
Factor 2527=19^{2}\times 7. Rewrite the square root of the product \sqrt{19^{2}\times 7} as the product of square roots \sqrt{19^{2}}\sqrt{7}. Take the square root of 19^{2}.
\frac{19\sqrt{7}\sqrt{10027}}{\left(\sqrt{10027}\right)^{2}}
Rationalize the denominator of \frac{19\sqrt{7}}{\sqrt{10027}} by multiplying numerator and denominator by \sqrt{10027}.
\frac{19\sqrt{7}\sqrt{10027}}{10027}
The square of \sqrt{10027} is 10027.
\frac{19\sqrt{70189}}{10027}
To multiply \sqrt{7} and \sqrt{10027}, multiply the numbers under the square root.
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