Without a calculator you would take steps.
Step 1: Narrow your squaring choices. Determine the two square roots that are primes of themselves and 1, on both greater and lesser sides of 7. So 4 and 9.
Step 2: Now we know you're looking for an answer that falls between 2*2 and 3*3. So you have to multiply decimals as a form of trial and error to find 7's square root. So I'd start at 2.5*2.5 and go from there.