Author Topic: Amazing Mental Maths!  (Read 6316 times)

Offline astarmathsandphysics

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Amazing Mental Maths!
« 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.
« Last Edit: August 09, 2010, 10:56:54 pm by DrEvil »

Offline past-papers

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Re: amazing mental maths
« Reply #1 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 / (3xn-12 + xn-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
« Last Edit: June 08, 2008, 01:01:05 am by past-papers »

master786

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Re: amazing mental maths
« Reply #2 on: June 08, 2008, 06:31:56 am »
which grade is all this done in :S..certainly not done within IGCSE limits:P
« Last Edit: June 08, 2008, 03:41:17 pm by master786 »

Offline past-papers

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Re: amazing mental maths
« Reply #3 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.

master786

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Re: amazing mental maths
« Reply #4 on: June 09, 2008, 06:34:56 pm »
:| wow :P
u r smart :D

Offline astarmathsandphysics

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Re: amazing mental maths
« Reply #5 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....

Offline past-papers

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Re: amazing mental maths
« Reply #6 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.

astatmathsanfphysics

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Re: amazing mental maths
« Reply #7 on: June 14, 2008, 04:46:58 pm »
ok past-papers but you you need a bit more than binomial expansion

nid404

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Re: amazing mental maths
« Reply #8 on: September 25, 2009, 10:54:48 am »
SO HOW IS IT DONE IN 30 SECOND??????

Offline Ghost Of Highbury

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Re: amazing mental maths
« Reply #9 on: September 25, 2009, 11:34:39 am »
how>?
divine intervention!

Offline Ghost Of Highbury

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Re: amazing mental maths
« Reply #10 on: September 25, 2009, 11:37:14 am »
3 - ((9-6)/2*3) = 3 - 0.5 = 2.5

actualy square root = 2.4
divine intervention!

Offline Ghost Of Highbury

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Re: amazing mental maths
« Reply #11 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
divine intervention!

nid404

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Re: amazing mental maths
« Reply #12 on: September 25, 2009, 11:51:43 am »
3 - ((9-6)/2*3) = 3 - 0.5 = 2.5

actualy square root = 2.4

didn't get the logic behind it

Offline Ghost Of Highbury

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Re: amazing mental maths
« Reply #13 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
divine intervention!

nid404

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Re: amazing mental maths
« Reply #14 on: September 25, 2009, 11:57:15 am »
oh ok