The only way to express the square root of 147 exactly is . Your computer's built-in calculator (both Windows and MAC O/Ss have them) will give you a numerical approximation to greater precision than you can ever practically use. Or you can SWAG it. 12 squared is 144 and 13 squared is 169, so the root of 147 has to be closer to 12 than 13. Calculate 12.1 squared and 12.2 squared: 146.41 and 148.84. So closer to 12.1 than 12.2...and so on. You can keep that up until you get enough decimal places to suit you. Write back once you get to calculus and have learned how to take a first derivative -- then we can do the Newton-Raphson method.
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it