x is an integer, and i can write it with $\log_2 x$ bit, and, viceversa, with $n$ bit i can write a number till $2^n$.. but.. how many bits to write $\sqrt x$ ?
EDIT: the integer part!
x is an integer, and i can write it with $\log_2 x$ bit, and, viceversa, with $n$ bit i can write a number till $2^n$.. but.. how many bits to write $\sqrt x$ ?
EDIT: the integer part!
If $\sqrt{x}$ is not an integer, it will take a lot of bits.
Hint: If it is an integer (or you are just writing the integer part) you should have a rule of logarithms that will help. Do you know another way to express $\sqrt{x}$?
$log_2 \sqrt n = log_2 n^{\frac{1}{2}} = \frac{1}{2} log_2 x$
thanks to Yuval Filmus and Ross Millikan for comments