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\sqrt{\frac{1024}{169}}
To multiply \sqrt{\frac{64}{9}} and \sqrt{\frac{144}{169}}, multiply the numbers under the square root.
\frac{32}{13}
Rewrite the square root of the division \frac{1024}{169} as the division of square roots \frac{\sqrt{1024}}{\sqrt{169}}. Take the square root of both numerator and denominator.