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$\begin{aligned} A_1 & = \sqrt{3} \\ A_2 & = \sqrt{A_1} \\ A_3 & = \sqrt{A_2} \\ & \vdots \\ A_{n+1} &= \sqrt{A_n} \end{aligned}$

What is the value of the infinite product $A_1 \times A_2 \times A_3\times \cdots \, ?$

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