Define a function $f(x)$ by \[f(x) = \left\{ \begin{aligned} \sqrt{x} & \quad \text{ if } \sqrt{x} \text{ is an integer}, \\ (f(x-1))^2 - 1 & \quad \text{ otherwise}. \end{aligned}\right.\]Compute $f(8).$
<|im_start|>system
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<|im_start|>user
Define a function $f(x)$ by \[f(x) = \left\{ \begin{aligned} \sqrt{x} & \quad \text{ if } \sqrt{x} \text{ is an integer}, \\ (f(x-1))^2 - 1 & \quad \text{ otherwise}. \end{aligned}\right.\]Compute $f(8).$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

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Define a function $f(x)$ by \[f(x) = \left\{ \begin{aligned} \sqrt{x} & \quad \text{ if } \sqrt{x} \text{ is an integer}, \\ (f(x-1))^2 - 1 & \quad \text{ otherwise}. \end{aligned}\right.\]Compute $f(8).$
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