Question

What is the square root of 129

Answer 1

If you are allowed to use a calculator then you only need to press the buttons. 

Assuming you cannot use a calculator you need to use approximation techniques. First let us begin by finding the two closest numbers that are perfect squares. In this case 11^2 and 12^2 are the closest square numbers to 129. 

11^2 = 121
12^2 = 144
We can already tell that the square root of 129 is closer to 11 than to 12. 
Now we need to get even closer.
If you try squaring a number like 11.5 then you can get even closer to 129. When you square 11.5 you get 132.25. Already you can tell that the square root of 129 is close to the square root of 132.25 or 11.5
Now we can get even closer square the number 11.25 and keep on going until one of these numbers when squared is almost or exactly 129. I hope I helped, there really isn't a great way to do this without a calculator, or by using the graph of y=x^2