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.

-- 
Saurabh Singh
B.Tech (Computer Science)
MNNIT ALLAHABAD

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