Is it possible to find square root using only rational numbers and elementary arithmetic operators Suppose I have a number a
How can I find it's square root using only +, -, /, * and rational numbers?
If it is impossible how to prove it?

When you use an infinite ammount of operations, you can use:
$$
    \!\ \sqrt{2} = 1 + \cfrac{1}{2 + \cfrac{1}{2 + \cfrac{1}{2 + \cfrac{1}{2 + \ddots}}}}. 
$$
from here...
