Calculate the numerical approximation of the square root of the desired number and estimate where it would be on the number line. , so, depending on the precision of your representation of a number line, pick a spot that would be close to that number and that's it. For example, if you just have a number line marked with whole numbers, then you would find a spot that is about 4 tenths of the way from the 1 to the 2, and then go just a little bit closer to 2, but certainly less than half-way from the 1 to the 2 and you will be close to the square root of 2 -- close enough anyway.
Since the square root of any number that is not a perfect square is irrational, no matter how precisely marked your number line, you cannot find the exact spot. All you can ever do is get as close as is necessary for the particular application.
