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General Chat NEW! The Student Forums Chatroom => Competitions => Topic started by: astarmathsandphysics on June 07, 2008, 11:50:59 pm

Title: Amazing Mental Maths!
Post by: astarmathsandphysics on June 07, 2008, 11:50:59 pm: Describe a method for working out the square root of a number to 6 significant figures. I can do it winside 30 seconds without paper working. Tell me how i do it.
Title: Re: amazing mental maths
Post by: past-papers on June 08, 2008, 12:58:14 am: Simple, use a calculator which gives answers to 6 significant figures.

Alternatively, you an use the Newton-Rafson convergence method. For example the roots of 3x³ + x² - 5x + 3 can be found by finding out that

x = 3 / (3x² + x - 5) therefore use the series x = 3 / (3x_n-1² + x_n-1 - 5)

and letting x = any number. The series should converge to a point which is known as the root.

This is how a calculator computes the root of something too by the way.

What's my prize?? ;D
Title: Re: amazing mental maths
Post by: master786 on June 08, 2008, 06:31:56 am: which grade is all this done in :S..certainly not done within IGCSE limits:P
Title: Re: amazing mental maths
Post by: past-papers on June 09, 2008, 04:52:49 pm: A-Level. Edexcel C3 will do the Newton Rafson method. You can use FP3 Taylor and Maclaurin's series' too bt they're more useful for working out the value of e and pi.
Title: Re: amazing mental maths
Post by: master786 on June 09, 2008, 06:34:56 pm: :| wow :P
u r smart :D
Title: Re: amazing mental maths
Post by: astarmathsandphysics on June 10, 2008, 06:23:30 pm: you're a wimp if you need to use a calulator and for newton raphson you need paper. So tell me....
Title: Re: amazing mental maths
Post by: past-papers on June 14, 2008, 04:34:36 pm: You can use Binomial Expansion with substitution if you want to too.

There are so many different ways of doing it man. The list is very long.
Title: Re: amazing mental maths
Post by: astatmathsanfphysics on June 14, 2008, 04:46:58 pm: ok past-papers but you you need a bit more than binomial expansion
Title: Re: amazing mental maths
Post by: nid404 on September 25, 2009, 10:54:48 am: SO HOW IS IT DONE IN 30 SECOND??????
Title: Re: amazing mental maths
Post by: Ghost Of Highbury on September 25, 2009, 11:34:39 am: how>?
Title: Re: amazing mental maths
Post by: Ghost Of Highbury on September 25, 2009, 11:37:14 am: 3 - ((9-6)/2*3) = 3 - 0.5 = 2.5

actualy square root = 2.4
Title: Re: amazing mental maths
Post by: Ghost Of Highbury on September 25, 2009, 11:50:30 am: for sqrt(19)

4 - ((16 - 19)/2*4) = 4.375

actual answer = 4.35

its a right method i guess

if so..whats my prize?!!?!?

:P
Title: Re: amazing mental maths
Post by: nid404 on September 25, 2009, 11:51:43 am: Quote from: eddie_adi619 on September 25, 2009, 11:37:14 am
3 - ((9-6)/2*3) = 3 - 0.5 = 2.5

actualy square root = 2.4

didn't get the logic behind it
Title: Re: amazing mental maths
Post by: Ghost Of Highbury on September 25, 2009, 11:56:11 am: $sqrt(6)$
know root close to 6 = 9

the formula

known root - $(known square - unknown square)/(2*known root)$

known root = 3 (of 9)

known square = 9
unknown square = 6

so...

$3 - (9-6)/(2*3)$ = $3 - 0.5$ = 2.5
Title: Re: amazing mental maths
Post by: nid404 on September 25, 2009, 11:57:15 am: oh ok
Title: Re: amazing mental maths
Post by: Ghost Of Highbury on September 25, 2009, 11:59:20 am: y doesnt the division symbol come up in the latex text..

i cud put the square root thingy though
Title: Re: amazing mental maths
Post by: astarmathsandphysics on September 25, 2009, 12:37:09 pm: To do x divided by y in latex type \frac {x}{y}
Title: Re: amazing mental maths
Post by: Ghost Of Highbury on September 25, 2009, 12:50:19 pm: $sqrt6$
know root close to 6 = 9

the formula

known root - $\frac {known square - unknown square}{2*known square root}$

known root = 3 (of 9)

known square = 9
unknown square = 6

so...

answer ==> 2.5
Title: Re: amazing mental maths
Post by: nid404 on September 27, 2009, 06:57:09 am: How do you get it in 6 d.p ......I wanna know to do it in 30 seconds....
Title: Re: amazing mental maths
Post by: Saladin on September 29, 2009, 07:07:17 am: Experience, practice and brains.
Title: Re: amazing mental maths
Post by: nid404 on September 29, 2009, 07:38:35 am: I know...I wanna start practicing...so how??