I can not figure out the answer to this greatest integer problem

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I can’t figure out the answer to this problem:

$$\left\lfloor\sqrt{\lfloor\pi\rfloor!}\right\rfloor=\;?$$

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Since $3\le\pi<4$, $\lfloor\pi\rfloor=3$, and $3!=3\cdot2\cdot1=6$, so we want $\left\lfloor\sqrt6\right\rfloor$. The square root of $6$ is between what two consecutive integers?