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GMATPrep - Square root question

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GMATPrep - Square root question [#permalink] New post 05 Aug 2008, 20:45
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The correct answer is 20, but I can't seem to get it.
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Re: GMATPrep - Square root question [#permalink] New post 05 Aug 2008, 21:34
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(sqrt(9 + sqrt(80)) + sqrt(9-sqrt(80)) ^2

1. (a+b)^2 = a^2 + 2ab + b^2

Thus we get:

sqrt(80) = 4*sqrt(5)

9 + 4*sqrt(5) + 2*(9+sqrt(80)) * (9 - sqrt(80)) + 9 - 4sqrt(5)

2. (9+sqrt(80)) * (9 - sqrt(80)) = 81 - 80 because (a+b) * (a-b) = a^2 - b^2

3. 4*sqrt(5) - 4*sqrt(5) = 0

4. Thus

9 + 2 + 9 = 20

-hth.
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Re: GMATPrep - Square root question [#permalink] New post 05 Aug 2008, 21:55
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Makes sense now...when I look back on my work, looks like I had a simple mistake when performing this calculation which was screwing me up...

(9 - sqrt(80)) = 81 - 80 because (a+b) * (a-b) = a^2 - b^2

Thanks!
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Re: GMATPrep - Square root question [#permalink] New post 06 Aug 2008, 01:56
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another way...
let 9=a and 80^1/2=b.
[looks complex , but on paper, its just 4 steps]

so the eqn is [(a+b)^1/2+(a-b)^1/2]^2. which is of the form [a+b]^2
on expanding, a+b+a-b+2[(a+b)(a-b)]^1/2.
we get 2a +2(a^2-b^2)^1/2
put the values back,
we get 18+2=20
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Re: GMATPrep - Square root question [#permalink] New post 06 Aug 2008, 16:23
pls help me with this.

9 + 4*sqrt(5) + 2*(9+sqrt(80)) * (9 - sqrt(80)) + 9 - 4sqrt(5)

Shouldn't the bold part be:

2*sqrt(9+sqrt(80)) * sqrt(9-sqrt(80)) ? - why did you get rid of your sqrt sign? How would this be multiplied out?

Thanks.

rahulm wrote:
(sqrt(9 + sqrt(80)) + sqrt(9-sqrt(80)) ^2

1. (a+b)^2 = a^2 + 2ab + b^2

Thus we get:

sqrt(80) = 4*sqrt(5)

9 + 4*sqrt(5) + 2*(9+sqrt(80)) * (9 - sqrt(80)) + 9 - 4sqrt(5)

2. (9+sqrt(80)) * (9 - sqrt(80)) = 81 - 80 because (a+b) * (a-b) = a^2 - b^2

3. 4*sqrt(5) - 4*sqrt(5) = 0

4. Thus

9 + 2 + 9 = 20

-hth.
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Re: GMATPrep - Square root question [#permalink] New post 11 Mar 2010, 01:40
miccarlo wrote:
The correct answer is 20, but I can't seem to get it.

(sqrt(9+sqrt80) + sqrt(9-sqrt80))^2

= 9+sqrt80 + 9-sqrt80 + 2 (9+sqrt80)(9-sqrt80) as (a+b)^2 = a^2+b^2+2ab
=18+2(81-80) as (a+b)(a-b) = a^2-b^2
=18+2
=20

so answer is 20
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Re: GMATPrep - Square root question [#permalink] New post 12 Mar 2010, 08:38
miccarlo wrote:
The correct answer is 20, but I can't seem to get it.


9-sqrt(80) + 9+-sqrt(80) + 2(sqrt((9-sqrt(80))(9+-sqrt(80)))
= 18 +2
=20
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Re: GMATPrep - Square root question [#permalink] New post 12 Mar 2010, 08:42
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bigfernhead wrote:
pls help me with this.

9 + 4*sqrt(5) + 2*(9+sqrt(80)) * (9 - sqrt(80)) + 9 - 4sqrt(5)

Shouldn't the bold part be:

2*sqrt(9+sqrt(80)) * sqrt(9-sqrt(80)) ? - why did you get rid of your sqrt sign? How would this be multiplied out?

Thanks.


Consider 9 as A
and sqrt(80) as B
so bold part reduces to 2*sqrt(A+B)*sqrt(A-B) = 2*sqrt((A+B)*(A-B)) = 2(sqrt(A^2 - B^2)) = 2(sqrt(81-80) = 2
Re: GMATPrep - Square root question   [#permalink] 12 Mar 2010, 08:42
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