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\frac{\sqrt{9}}{\sqrt{314}}
Rewrite the square root of the division \sqrt{\frac{9}{314}} as the division of square roots \frac{\sqrt{9}}{\sqrt{314}}.
\frac{3}{\sqrt{314}}
Calculate the square root of 9 and get 3.
\frac{3\sqrt{314}}{\left(\sqrt{314}\right)^{2}}
Rationalize the denominator of \frac{3}{\sqrt{314}} by multiplying numerator and denominator by \sqrt{314}.
\frac{3\sqrt{314}}{314}
The square of \sqrt{314} is 314.