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SQRT(12+√44)-SQRT(12-√44) =

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laxieqv
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SQRT(12+√44)-SQRT(12-√44) = [#permalink] New post   29 Dec 2005, 02:10
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SQRT(12+√44)-SQRT(12-√44) = ?



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Re: SQRT(12+√44)-SQRT(12-√44) = [#permalink] New post   29 Dec 2005, 04:04
I don't know how to simplify further:

sqrt2 [sqrt(6+sqrt11) - sqrt(6-sqrt11)], the marked part has to be sqrt2, but how?
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Re: SQRT(12+√44)-SQRT(12-√44) = [#permalink] New post   29 Dec 2005, 04:10
I think GMAT may test this typical problem :P . Let wait for some more responses first, okie?! :wink:
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Re: SQRT(12+√44)-SQRT(12-√44) = [#permalink] New post   29 Dec 2005, 09:22
The answer is 2
SQRT(12+√44)-SQRT(12-√44) = 2

I solved by the substituting approximate values for sqrt(44) as we know sqrt(49) is 7

= Sqrt( 12 + 6.6) - sqrt( 12-6.6)
= sqrt(18.6) - sqrt(5.3)
~ 4.3-2.3 = 2

Sure there should be another way of solving it,.. But I found this fast & easy
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Re: SQRT(12+√44)-SQRT(12-√44) = [#permalink] New post   29 Dec 2005, 13:37
Good Question

I will try like this:

a=12, b=sqrt44.

so sqrt (a+b)-sqrt(a-b)
=sqrt (a+b-a+b)
= sqrt(2b)
=sqrt[2sqrt44]
=sqrt[2*2sqrt11]
2sqrt.sqrt11 =

2(4root11)
laxieqv wrote:
SQRT(12+√44)-SQRT(12-√44) = ?
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Re: SQRT(12+√44)-SQRT(12-√44) = [#permalink] New post   29 Dec 2005, 20:53
laxieqv wrote:
SQRT(12+√44)-SQRT(12-√44) = ?




sqrt(12+sqrt44)= sqrt( 11+ 2sqrt11 +1) = sqrt[(sqrt11+1)]^2= sqrt11+1
similarly, sqrt(12-sqrt44)= sqrt11-1

---> the sum= sqrt11+1 - (sqrt11 -1)= 2
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Re: SQRT(12+√44)-SQRT(12-√44) = [#permalink] New post   29 Dec 2005, 21:56
:lol: got it right, although different approach..

Think I am gradually progressing on my prep.
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Re: SQRT(12+√44)-SQRT(12-√44) = [#permalink] New post   29 Dec 2005, 23:54
Itzrevs wrote:
:lol: got it right, although different approach..

Think I am gradually progressing on my prep.


your approximation method is creative :wink:
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Re: SQRT(12+√44)-SQRT(12-√44) = [#permalink] New post   30 Dec 2005, 04:47
laxieqv wrote:
laxieqv wrote:
SQRT(12+√44)-SQRT(12-√44) = ?




sqrt(12+sqrt44)= sqrt( 11+ 2sqrt11 +1) = sqrt[(sqrt11+1)]^2= sqrt11+1
similarly, sqrt(12-sqrt44)= sqrt11-1

---> the sum= sqrt11+1 - (sqrt11 -1)= 2


:good



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Re: SQRT(12+√44)-SQRT(12-√44) = [#permalink]
30 Dec 2005, 04:47
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