I was wondering can we design a machine(Even hypothetical) that can find a *perfect square root *of any integer thats given to it. My logic why we can't is since there are uncountably infinite real numbers, there will be uncountably infinite numbers requiring infinite states on a turing machine.But since there are only finite number of states,we cant make such a machine.And since we cant make a turing machine for calculating the square root we cant make any computing machine for the same. I am not sure about my logic though.Thats why i have this doubt.
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