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\sqrt{\frac{4}{225}}
To multiply \sqrt{\frac{2}{3}} and \sqrt{\frac{2}{75}}, multiply the numbers under the square root.
\frac{2}{15}
Rewrite the square root of the division \frac{4}{225} as the division of square roots \frac{\sqrt{4}}{\sqrt{225}}. Take the square root of both numerator and denominator.