Question

55 points PLEASE HELP

If you use the Babylonian method to estimate the square root of 70 to the nearest hundredth, starting with the estimate 8, what is the next estimate? 8.3 8.38 16.75 8.4

Answer 1

The formula is Square Root (Given number) = (previous estimate + Given number/previous estimate) /2
Remark
To think this was known 3600 years ago. Fascinating. thanks for posting.
So your first guess was 8.

Givens
Given number = 70 which for this question, you always use)
Previoius Estimate = 8

Sub and solve
(8 + 70/8 ) /2 = 8.375 which using their rounding system is 8.38

Remark
This is a wonderful example of iteration which computers use all the time.

Answer 2

The Babylonian method uses the following formula:

n₁ = (n₀ + (s ÷ n₀)) / 2

n₀ represents your original estimate, s represents the number that you're trying to find the square root of, and n₁ represents the next estimate.

Plug your values into the equation:

n₀ = 8
s = 70


`(8 + (70 / 8)) / 2`


`(8 + 8.75) / 2`


`16.75 / 2 = 8.375`

Round this number to the nearest hundredths value:


`8.375`

`5 = 5`

`8.375 \approx 8.38`

The answer is 8.38.