Answer: 13.2300 is the next guess
To use the Babylonian method, you first start with your guess of 13.0463. Then, you add to it the original number divided by 13.0463.
It would look like this:
13.0463 + 175/13.0463 =26.460006
Then, you divide this number by 2.
The result is 13.2300
This value is closer to the correct square root of 175.