Square Roots

[The Cat]

Do any of you guys know how to find the square root of any number without using a calculator?

[Parrakarry]

Ehh, kind of. Gotta divide and average or something like that. My algebra teacher told me how, but I don't remember EXACTLY... here, lemme look it up.

Ah, here it is:

To find sqrt of 5:

FIRST PROCESS

Step 1: Guess 2 (because 2*2=4, close to 5)

Step 2: Divide 5 by 2 = 2.5

Step 3: Find average of 2 and 2.5 = 2.25 (because (2+2.5)/2 = 2.25)

Step 4: Next guess is 2.25

SECOND PROCESS

Step 1: Guess 2.25

Step 2: Divide 5 by 2.25 = 2.22222222 (go 8 decimal places for accuracy)

Step 3: Find average of 2.25 and 2.22222222 = 2.23611111

Step 4: Next guess is 2.23611111

THIRD PROCESS

Step 1: Guess 2.236111111

Step 2: Divide 5 by 2.23611111 = 2.2360248

Step 3: Find average of 2.23611111 and 2.2360248 = 2.2360679

Step 4: FINAL guess is 2.2360679

Now CHECK your final guess with a calculator: sqrt 5 = 2.2360679

[The Cat]

K, thanks, because my calculator broke. :(

Still, I don't the idea of using trial and error to find a square root, but I guess it's the only method that works.

[Parrakarry]

Ahh, but it's NOT trial and error. That's the exact equation your calculator performs to do a square root, too. Just a lot harder. XD

[Dux is not you]

Dunno, but there's still "Calculator" on the Start Menu. Are you not using Windows or something?

[UserGoogol]

It's not an equation, it's an algorithm.

Hmnm, but I'm not sure if calculators and computers use that method. There's probably a faster method than your algorithm.

There's a long-division-esque algorithm explained here and elsewhere. It's much easier on humans than Parrakarry's method.

[Parrakarry]

Blah. Equation, algorithm.

[Dark Magus]

Originally posted by Sidestream Dux:
Dunno, but there's still "Calculator" on the Start Menu. Are you not using Windows or something?

Good luck bringing your Start Menu to school with you.