Evaluate
\frac{10\sqrt{157}}{157}\approx 0.798086884
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\sqrt{\frac{200}{314}}
Expand \frac{2}{3.14} by multiplying both numerator and the denominator by 100.
\sqrt{\frac{100}{157}}
Reduce the fraction \frac{200}{314} to lowest terms by extracting and canceling out 2.
\frac{\sqrt{100}}{\sqrt{157}}
Rewrite the square root of the division \sqrt{\frac{100}{157}} as the division of square roots \frac{\sqrt{100}}{\sqrt{157}}.
\frac{10}{\sqrt{157}}
Calculate the square root of 100 and get 10.
\frac{10\sqrt{157}}{\left(\sqrt{157}\right)^{2}}
Rationalize the denominator of \frac{10}{\sqrt{157}} by multiplying numerator and denominator by \sqrt{157}.
\frac{10\sqrt{157}}{157}
The square of \sqrt{157} is 157.
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