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?

The set of rational numbers is closed under the elementary arithmetic operations (except for division by zero), i.e. if you have two rational numbers and take their sum, difference, product, or quotient, then the result is again a rational number (again, except for division by zero). Since $\sqrt{a}$ can fail to be a rational number (say, $\sqrt{2}$), there is no formula for $\sqrt{a}$ involving only elementary arithmetic operations.
Proof link
