SOLUTION: What is simple solution of root 5 Wht is way to solve that prob rasily

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Question 901036: What is simple solution of root 5
Wht is way to solve that prob rasily
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
2%5E2=4
r%5E2=5
3%5E2=9

A simple way to find r is try to take averages and pick the approximation that gives result of 5 as close as you want. Start with average of 2 and 3 and test this.

%282%2B3%29%2F2=5%2F2.
%285%2F2%29%5E2=25%2F4=6%261%2F4--- too high.

Find average of 2 and 5/2.
%282%2B5%2F2%29%2F2=%284%2F2%2B5%2F2%29%2F2=9%2F4.
%289%2F4%29%5E2=36%2F16=2%261%2F4--- too low.

Try between 2.25 and 5/2.
(9/4+5/2)/2=(9/4+10/4)/2=19/(4*2)
19%2F8
-
%2819%2F8%29%5E2=5.640625----too high
-
Try 19/10.
%2819%2F10%29%5E2=3.61----too low

Next you can try something between 19/10 and 19/8,
maybe try 19/9.
%2819%2F9%29%5E2=4.4568----too low.

You would want between 19/9 and 19/8;
Find their average, and test.
Average of 38/18 and 38/16....
continue this process if you want...

Another way is to use table of logarithms; which could be easy but "simple" depends on how comfortable you are with doing this.


Actually, 2.24 is fairly close to sqrt%285%29.
2.24%5E2=5.0176
and
2.235%5E2=4.9952