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\sqrt{\frac{1}{9}}
To multiply \sqrt{\frac{2}{27}} and \sqrt{\frac{3}{2}}, multiply the numbers under the square root.
\frac{1}{3}
Rewrite the square root of the division \frac{1}{9} as the division of square roots \frac{\sqrt{1}}{\sqrt{9}}. Take the square root of both numerator and denominator.