IGCSE/GCSE/O & A Level/IB/University Student Forum
General Chat NEW! The Student Forums Chatroom => Competitions => Topic started 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.

Simple, use a calculator which gives answers to 6 significant figures.
Alternatively, you an use the NewtonRafson convergence method. For example the roots of 3x^{3} + x^{2}  5x + 3 can be found by finding out that
x = 3 / (3x^{2} + x  5) therefore use the series x = 3 / (3x_{n1}^{2} + x_{n1}  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

which grade is all this done in :S..certainly not done within IGCSE limits:P

ALevel. 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.

: wow :P
u r smart :D

you're a wimp if you need to use a calulator and for newton raphson you need paper. So tell me....

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.

ok pastpapers but you you need a bit more than binomial expansion

SO HOW IS IT DONE IN 30 SECOND??????

how>?

3  ((96)/2*3) = 3  0.5 = 2.5
actualy square root = 2.4

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

3  ((96)/2*3) = 3  0.5 = 2.5
actualy square root = 2.4
didn't get the logic behind it

know root close to 6 = 9
the formula
known root 
known root = 3 (of 9)
known square = 9
unknown square = 6
so...
= = 2.5

oh ok

y doesnt the division symbol come up in the latex text..
i cud put the square root thingy though

To do x divided by y in latex type \frac {x}{y}

know root close to 6 = 9
the formula
known root 
known root = 3 (of 9)
known square = 9
unknown square = 6
so...
answer ==> 2.5

How do you get it in 6 d.p ......I wanna know to do it in 30 seconds....

Experience, practice and brains.

I know...I wanna start practicing...so how??