Question

Got an odd lil question... can I get some help?
~> Suppose you have a scientific calculator where some of the buttons are broken. In fact the only working keys are the digits [0] to [9], [+],[-],[x],[/] and [e^x] and [ln]. Explain how you can use this calculator to calculate the square root of any whole number.

Answer 1

some numbers ln divide some number = e^x

Answer 2

yeah but we dont have ln

Answer 3

Oh crap

Answer 4

this page explains the Babylonian method. It's basically making an educated guess and fine tuning that guess to get more accurate results

http://www.deltacollege.edu/dept/basicmath/Babylonian.htm

Answer 5

Ooh nice Jim.

Answer 6

comeonn guyss...

Answer 7

and you call yourselves professors of mathematics

Answer 8

:p

Answer 9

that page has all the answers you need

Answer 10

it was something to do with using indirectly using ln

Answer 11

and it wasn't an estimate :/

Answer 12

on that page, they have the example of sqrt(5)

a good guess is 2. Divide 5 by 2 to get

5/2 = 2.5

then notice how 2*2 = 4 is too small and 2.5*2.5 = 6.25 is too big. So the value of sqrt(5) is between 2 and 2.5

average the two:

(2+2.5)/2 = 2.25

then you repeat the process all over again with the new guess of 2.25

Answer 13

i "guess" that works :p

Answer 14

well I guess you can say

\[\Large \sqrt{x} = x^{1/2}\]

but I don't know how to tie it in with \(\Large e^x\) or natural logs. So I'd just stick with the Babylonian method.

Answer 15

how about if you had [ln]?

Answer 16

it's okay guys don't fry your brains :p

Answer 17

still don't know, but I'll think it over

Answer 18

should be easy if you have [ln]

Answer 19

okay thanks anyways <3

Answer 20

oh noes

Answer 21

I believe in you :)

Answer 22

ok if you had both e^x and ln(x) buttons, then you can do this

\[\Large \sqrt{x} = e^{\ln(\sqrt{x})} \]

\[\Large \sqrt{x} = e^{\ln(x^{1/2})} \]

\[\Large \sqrt{x} = e^{\frac{1}{2}\ln(x)} \]

-------------------------------------------------------

So for example,

\[\Large \sqrt{x} = e^{\frac{1}{2}\ln(x)} \]

\[\Large \sqrt{5} = e^{\frac{1}{2}\ln(5)} \]

\[\Large \sqrt{5} \approx 2.23606797750042 \]

Answer 23

now wasn't that simple :p