solution: We find that $f(1) = 2^1 = 2.$ Then, $f(f(1)) = f(2) = 2^2 = 4$ and $f(f(f(1))) = f(4) = 2^4 = 16.$ Therefore, $f(f(f(f(1)))) = f(16) = 2^{16}$ and so $\sqrt{f(f(f(f(1))))} = \sqrt{2^{16}} = 2^8 = \boxed{256}.$
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  Let $f(x) = 2^x.$ Find $\sqrt{f(f(f(f(1))))}.$
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: 256
extra_info.question: Let $f(x) = 2^x.$ Find $\sqrt{f(f(f(f(1))))}.$
extra_info.split: test