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\sqrt[6]{27}=\sqrt[6]{3^{3}}=3^{\frac{3}{6}}=3^{\frac{1}{2}}=\sqrt{3}
Rewrite \sqrt[6]{27} as \sqrt[6]{3^{3}}. Convert from radical to exponential form and cancel out 3 in the exponent. Convert back to radical form.
\left(\sqrt{3}\right)^{2}
Insert the obtained value back in the expression.
3
The square of \sqrt{3} is 3.