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\sqrt{\frac{9}{19}}
Reduce the fraction \frac{45}{95} to lowest terms by extracting and canceling out 5.
\frac{\sqrt{9}}{\sqrt{19}}
Rewrite the square root of the division \sqrt{\frac{9}{19}} as the division of square roots \frac{\sqrt{9}}{\sqrt{19}}.
\frac{3}{\sqrt{19}}
Calculate the square root of 9 and get 3.
\frac{3\sqrt{19}}{\left(\sqrt{19}\right)^{2}}
Rationalize the denominator of \frac{3}{\sqrt{19}} by multiplying numerator and denominator by \sqrt{19}.
\frac{3\sqrt{19}}{19}
The square of \sqrt{19} is 19.