November Math Problem

[terminator]

Square root of 1737.1737 within +- .5% error.

Cannot use a calculator to solve.
Must show work on how it was done algebriacally (No guess and check)


I solved it in two ways so it is possible


Terms method rendered the answer 41.68096747241 (0.003722915815% Error) So it is possible! This is more about the process then answer!)

This is more asking what formula is √x~=?

*Note I did use a calculator afterword to plug in values to save time, but I could have done it freehand, that is the point of this )

[Leone]

I think the answer is 41.68.

Please show your working out:

I copied Termy's post(!)

[Gullander]

I lost my sliderule in the early to mid 70's when TI came out with calculators! Oh...that would be cheating wouldn't it.

[terminator]

I lost my sliderule in the early to mid 70's when TI came out with calculators! Oh...that would be cheating wouldn't it.

^^ xD

[WARBRINGER]

Face it termi, you're the mathematics genius here, not us!

[LostKnight]

Face it termi, you're the mathematics genius here, not us!

+1

OK I cheated and used math

Code: Select all

   $ math
> sqrt(1737.1737)
41.679415783
> 41.679415783*41.679415783
1737.173700012

[SellSword]

I avoided questions like this by going to law school. That's my answer!

[Gullander]

Hmmm...I really don't recall any formula for determining square roots other than the trial and error of multiplying what fits in. In this case 40x40 is 1600 so not enough...41 x 41 is 1681 so not enough still, 42 x 42 1764 so somewhere between 41 and 42. So keep factoring in digits after 41 whittling the total down till as close as possible. If there is a way to minimize the reasoned guesswork it eludes me, but alas it has been very long ago.

I got to thinking you could divide it up perhaps? A way you could use the addition of square roots to get the square root for the big number?
Put that to the test and no! the remaining number may give you a clue as to the next digit but doesn't math out
for instance 1737 -1681 is 56...which would be a square of 7 or 49 as the closest...but we know the next digits are .68 so this is wrong approach for exactness

[WARBRINGER]

Here I was thinking A-level maths looked hard

[LostKnight]

GUGL says thinK:

Code: Select all

             .
         ----------
        /1737.1737
20+_=00 /

but again I cheated.