Question

Someone tell me how to do the Babylonian Method?

Answer 1

LOL the x kinda scared me for a sec, I thought my question was like.. denied XD

Answer 2

Okay, for whatever number \(S\) you are trying to square root, make a guess and call it \(x_0\). You can make a close guess by noticing what perfect square is near \(S\). Then, take your \(x_0\) and average it with \(\dfrac{S}{x_0}\). Call the result \(x_1\). Repeat the process until you get close enough to your square root.

Example: Let's take the square root of 30. We can see that it's between the squares of 5 and 6, so let's guess an \(x_0\) of 5. So, we find our \(x_1\) by averaging 5 and \(\dfrac{30}{5}\). That will give us 5.5. Then we repeat the process. Average 5.5 with \(\dfrac{30}{5.5}\) That gives us about 5.477. One more time, average 5.477 with \(\dfrac{30}{5.477}\). This gives us back 5.477 again! If we were being more precise (using more decimals) it would have changed to be a bit more precise, but at four significant figures it will continue to give us back 5.477. Sure enough, if you check your calculator, the square root of 30 is approximately 5.477.

Answer 3

ohh, I see.
but, in my school, theres something a lil different:



solve for r^1