Question

When using the Babylonian method to approximate √5 if you start with a guess of 2, then what will be your next guess?

A.
2.25

B.
2.5

C.
3

D.
2

Answer 1

The Babylonian method is
\[x_{n+1}=\frac{1}{2}\left(x_n+\frac{a}{x_n}\right)\]
where a is the number whose square root you're looking for, right?

Answer 2

Since a=5 and x_0=2, your next guess is
\[x_1=\frac{1}{2}\left(2+\frac{5}{2}\right)\]
If you plug this in your calculator, you should get the right answer.