Amazing Mental Maths!

[astarmathsandphysics]

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.

[past-papers]

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??

[master786]

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

[past-papers]

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]

:| wow
u r smart

[astarmathsandphysics]

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

[past-papers]

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]

ok past-papers but you you need a bit more than binomial expansion

[nid404]

SO HOW IS IT DONE IN 30 SECOND???

[Ghost Of Highbury]

how>?

[Ghost Of Highbury]

3 - ((9-6)/2*3) = 3 - 0.5 = 2.5

actualy square root = 2.4

[Ghost Of Highbury]

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?!!?!?

[nid404]

3 - ((9-6)/2*3) = 3 - 0.5 = 2.5

actualy square root = 2.4

didn't get the logic behind it

[Ghost Of Highbury]

know root close to 6 = 9

the formula

known root  -

known root = 3 (of 9)

known square = 9
unknown square = 6

so...

= = 2.5

[nid404]

oh ok