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\frac{\sqrt{7145}}{\sqrt{341}}
Rewrite the square root of the division \sqrt{\frac{7145}{341}} as the division of square roots \frac{\sqrt{7145}}{\sqrt{341}}.
\frac{\sqrt{7145}\sqrt{341}}{\left(\sqrt{341}\right)^{2}}
Rationalize the denominator of \frac{\sqrt{7145}}{\sqrt{341}} by multiplying numerator and denominator by \sqrt{341}.
\frac{\sqrt{7145}\sqrt{341}}{341}
The square of \sqrt{341} is 341.
\frac{\sqrt{2436445}}{341}
To multiply \sqrt{7145} and \sqrt{341}, multiply the numbers under the square root.