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\sqrt{\frac{-2\left(-2\right)}{9}}
Express -\frac{2}{9}\left(-2\right) as a single fraction.
\sqrt{\frac{4}{9}}
Multiply -2 and -2 to get 4.
\frac{2}{3}
Rewrite the square root of the division \frac{4}{9} as the division of square roots \frac{\sqrt{4}}{\sqrt{9}}. Take the square root of both numerator and denominator.