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\frac{\sqrt{23}}{\sqrt{15}}
Rewrite the square root of the division \sqrt{\frac{23}{15}} as the division of square roots \frac{\sqrt{23}}{\sqrt{15}}.
\frac{\sqrt{23}\sqrt{15}}{\left(\sqrt{15}\right)^{2}}
Rationalize the denominator of \frac{\sqrt{23}}{\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.
\frac{\sqrt{23}\sqrt{15}}{15}
The square of \sqrt{15} is 15.
\frac{\sqrt{345}}{15}
To multiply \sqrt{23} and \sqrt{15}, multiply the numbers under the square root.