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\frac{\sqrt{138}}{\sqrt{29}}
Rewrite the square root of the division \sqrt{\frac{138}{29}} as the division of square roots \frac{\sqrt{138}}{\sqrt{29}}.
\frac{\sqrt{138}\sqrt{29}}{\left(\sqrt{29}\right)^{2}}
Rationalize the denominator of \frac{\sqrt{138}}{\sqrt{29}} by multiplying numerator and denominator by \sqrt{29}.
\frac{\sqrt{138}\sqrt{29}}{29}
The square of \sqrt{29} is 29.
\frac{\sqrt{4002}}{29}
To multiply \sqrt{138} and \sqrt{29}, multiply the numbers under the square root.