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\frac{\sqrt{2}}{\sqrt{3}}\sqrt{27}
Rewrite the square root of the division \sqrt{\frac{2}{3}} as the division of square roots \frac{\sqrt{2}}{\sqrt{3}}.
\frac{\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\sqrt{27}
Rationalize the denominator of \frac{\sqrt{2}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.
\frac{\sqrt{2}\sqrt{3}}{3}\sqrt{27}
The square of \sqrt{3} is 3.
\frac{\sqrt{6}}{3}\sqrt{27}
To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.
\frac{\sqrt{6}}{3}\times 3\sqrt{3}
Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.
\sqrt{6}\sqrt{3}
Cancel out 3 and 3.
\sqrt{3}\sqrt{2}\sqrt{3}
Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.
3\sqrt{2}
Multiply \sqrt{3} and \sqrt{3} to get 3.