The best way to solve square roots of say less than 1000 is by trial and error.
It is easiest to start with multiples of 10 and see the value of their squares. For example:
10^2 = 100
20^2 = 400
30^2 = 900
Now we know that the square root of 625 must be somewhere between 20 and 30. Now we must try values between 20 and 30 to see whether their square are near to 625.
It is often easiest to start with a number halfway between the two your are looking at, so let's try 25:
25^2 = 625.
And we've found it!
In this case, we were lucky that the number we decided to pick between 20 and 30 gave us the right answer. If it hadn't have given us the answer we were looking for we would do the same process as before, finding another two numbers closer together which our square root was between and continuing in this way until we got to the number we were looking for.