Find the perfect squares that are closest to the number. For instance, if you have √12, the closest perfect squares are 9 and 16.
Estimate a value between the square roots of the two closest perfect squares. In this case the square roots of 9 and 16 are 3 and 4. Therefore, you would estimate a value between 3 and 4 for √12. You could start with 3.5.
Square your estimate to see if you are accurate. In this case you would multiply 3.5 times 3.5 to get 12.25, which is a little too high.
Revise your estimate and multiply again. Continue to do this until you find an acceptably accurate answer. In this case, you might try 3.4 times 3.4, which equals 11.56. You would keep narrowing your estimates until you came to 3.465 as the square root of 12.