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Expansion

By using a suitable type of expansion; approximate √24, to 1.d.p.

Rep will be given. :cool:
√24 = 2√6

√6 = (5+1)1/2 = (√5)(1+1/5)1/2

√24 = (2√5)(1+1/5)1/2

and then expand (1+1/5)1/2 ?

EDIT: sorry that's balls cos of the √5.
Reply 2
Avatar for Dekota
Dekota
OP
wacabac
EDIT: sorry that's balls cos of the √5.


Carry on ... say is this right ..

√24 = 2√6

√6 = √(5+1) = (√5)√(1+1/5)

√24 = (2√5)√(1+1/5)

√24 = (2√(4+1))√(1+1/5)

√24 = (2√(4(1+¼)))√(1+1/5)

√24 = 4√(1+¼)√(1+1/5)

and so expand √(1+¼) and √(1+1/5) ?
V.P. Keys
Carry on ... say is this right ..

√24 = 2√6

√6 = √(5+1) = (√5)√(1+1/5)

√24 = (2√5)√(1+1/5)

√24 = (2√(4+1))√(1+1/5)

√24 = (2√(4(1+¼)))√(1+1/5)

√24 = 4√(1+¼)√(1+1/5)

and so expand √(1+¼) and √(1+1/5) ?


You can simplify it further to:

√24 = 4√(1+¼)√(1+1/5)

= 4√[(1+¼)(1+1/5)]

= 4√(1+1/2)
Reply 4
Avatar for Dekota
Dekota
OP
wacabac
You can simplify it further to:

√24 = 4√(1+1/2)


:biggrin: That is cool!! My maths teacher says you can't use binomial expansions to get approximations for numbers greater than 1. So:

(1+x)^n = 1 + nx + n(n-1)/2!x² ... Is only valid for |x| < 1

So I thought, there is no way I can do say &#8730;34 or &#8730;24 by manipulation, and the guy goes; no.
I proved him wrong. :cool:
Indeed you have!
V.P. Keys
By using a suitable type of expansion; approximate &#8730;24, to 1.d.p.

Rep will be given. :cool:

&#8730;24
= &#8730;6.&#8730;4
= 2&#8730;6
= 2[5(1+1/5)]1/2
= 2&#8730;5(1+1/5)1/2
= 2[4(1+1/4)]1/2(1+1/5))1/2
= 2&#8730;4(1+1/4)1/2(1+1/5))1/2
= 4(1+1/4)(1+1/5)1/2
= 4(1+1/2)1/2
= 4(1 + (½)(½) + (½)(-½)(½)²/2! + ....)
= 4(1+¼-1/32+....)
= 4(39/32)
= 156/32 &#8776;4.9 (1d.p)

I think in a C4 exam (as they usually do :rolleyes: ) they'd lead you through this one baby maths style and probably ask for the answer to 2 dp as well.
Reply 7
Avatar for steve2005
steve2005
17
Widowmaker

= 4(39/32)
= 156/32 ?4.9 (1d.p)

I think in a C4 exam (as they usually do :rolleyes: ) they'd lead you through this one baby maths style and probably ask for the answer to 2 dp as well.


Widowmaker... u beat me. But I did it before I saw your post.
Picture 11.png31.7KB
Reply 8
Avatar for Dekota
Dekota
OP
I like it! :biggrin:

Thanks all of you.
I'd advise going for an extra term in the expansion.
wacabac
I'd advise going for an extra term in the expansion.

Why?
4.9² = 24.01
Sorry, no you're right, my brain is all muddled, misread calculator blah blah blah urrrrrrrrrgh.

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