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\sqrt{\frac{61}{10}}
Reduce the fraction \frac{549}{90} to lowest terms by extracting and canceling out 9.
\frac{\sqrt{61}}{\sqrt{10}}
Rewrite the square root of the division \sqrt{\frac{61}{10}} as the division of square roots \frac{\sqrt{61}}{\sqrt{10}}.
\frac{\sqrt{61}\sqrt{10}}{\left(\sqrt{10}\right)^{2}}
Rationalize the denominator of \frac{\sqrt{61}}{\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.
\frac{\sqrt{61}\sqrt{10}}{10}
The square of \sqrt{10} is 10.
\frac{\sqrt{610}}{10}
To multiply \sqrt{61} and \sqrt{10}, multiply the numbers under the square root.