Question

There are 7 square roots.

(1) sqrt40
(2) sqrt75
(3) sqrt90
(4) sqrt245
(5) sqrt450
(6) sqrt640
(7) sqrt675

My assignment is to estimate the values of these square roots.
I am allowed to estimate using either the Babylonian Method or the Table Method.
I have no idea how to solve this. I'd be really happy if one of the square roots would be solved (step by step, every detail shown), so that I could understand how to solve the rest. I would also love it if someone would explain the difference between the two methods. Thank you very much.

Answer 1

e.g. √245 = x

first guess: x = 15
245/15 = 16.33333
average with previous guess:
(15+16.33333..)/2 = 15.6666.. <---- new guess

245/15.6666.. = 15.63829..
average with previous guess:
(15.6666.. + 15.63829..)/2 = 15.65248...

245/15.65248 = 15.65246...
average with previous guess:
(15.65248.. + 15.65246..)/2 = 15.65247584

no change in the first 4 decimals

Using the √ key
√245 = 15.65247584
Wow!, how is that ???

Don't know what kind of tables you have.