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\sqrt{\frac{323}{21}}
To multiply \sqrt{\frac{17}{7}} and \sqrt{\frac{19}{3}}, multiply the numbers under the square root.
\frac{\sqrt{323}}{\sqrt{21}}
Rewrite the square root of the division \sqrt{\frac{323}{21}} as the division of square roots \frac{\sqrt{323}}{\sqrt{21}}.
\frac{\sqrt{323}\sqrt{21}}{\left(\sqrt{21}\right)^{2}}
Rationalize the denominator of \frac{\sqrt{323}}{\sqrt{21}} by multiplying numerator and denominator by \sqrt{21}.
\frac{\sqrt{323}\sqrt{21}}{21}
The square of \sqrt{21} is 21.
\frac{\sqrt{6783}}{21}
To multiply \sqrt{323} and \sqrt{21}, multiply the numbers under the square root.