Sums of roots to approximate numbers I was thinking about random sequences, and thought up of this problem. 
Can algebraic or rational be expressed as a sum or difference of integer square roots? 
For example, $5=\sqrt{25}=\sqrt{16}+\sqrt{1}$.
It is known that if the series is infinite any number can be approximated, but is it possible to get any algebraic number(rational or irrational) with a FINITE number of terms? 

Any finite sum or difference of integer square roots is an algebraic number, and $\pi$ is known to be transcendental.  So it is not possible
