Question

Use the Babylonian method to approximate sqrt 19  to the nearest hundredth.

Answer 1

hi!!

Answer 2

Hello

Answer 3

first make a guess. i guess 4, which is not too close, because \(4^2=16\) but close enough

Answer 4

then for the "babylonian"method the next guess is the average of 4 and 19/4 i.e.
\[\frac{1}{2}(4+\frac{19}{4})\]

Answer 5

i get
\[\frac{35}{8}\] or
\[4.375\]

Answer 6

for the next one, you repeat the process, only with \(4.375\) instead of 4 i.e.
\[\frac{1}{2}(4.375+\frac{19}{4.375})\] at this point you want a calculator

Answer 7

then do it again etc
should be correct to two decimal places in only 3 tries or so