Most square roots are irrational. Here, Let's try this. This works for a few numbers.

Take a number, and take the square of it. Keep this number. Subtract one from it, and take the square root. If it is not irrational, take the number, and add one, and do the same. Keep adding, or subtracting, until you've added or subtracted the same number, that you originally used.

So if I take 3, squared, that is 9. So subtract one, that is 8. Say that was not irrational. I add one. If it is still rational, I subtract/add two this time. If it is still rational, I subtract/add 3.

This is a good tutorial of how to find the number without a calculator:

http://www.homeschoolmath.net/teaching/square-root-algorithm.php

Square roots are very good at irrational numbers. Have fun!!!