Determine which of $\displaystyle {\left(\frac{1}{2}e\right)}^{\sqrt{3}}$ and $\displaystyle \left(\sqrt{2}\right)^{\frac{1}{2}\pi}$ is greater.
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$\displaystyle {\left(\frac{1}{2}e\right)}^{\sqrt{3}}$ = 1.70145654213 $\displaystyle \left(\sqrt{2}\right)^{\frac{1}{2}\pi}$ = 1.72356793413
sorry... I should have added "without a calculator"
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