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# GMATPrep - Square root question

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Manager
Joined: 17 Mar 2007
Posts: 126
Location: San Francisco, CA
Schools: Haas, Booth, Kellogg, Stanford
GMATPrep - Square root question [#permalink]

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05 Aug 2008, 21:45
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Difficulty:

(N/A)

Question Stats:

100% (03:48) correct 0% (00:00) wrong based on 2 sessions

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The correct answer is 20, but I can't seem to get it.
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Intern
Joined: 03 Sep 2007
Posts: 13
Re: GMATPrep - Square root question [#permalink]

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05 Aug 2008, 22:34
1
KUDOS
(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.
Manager
Joined: 17 Mar 2007
Posts: 126
Location: San Francisco, CA
Schools: Haas, Booth, Kellogg, Stanford
Re: GMATPrep - Square root question [#permalink]

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05 Aug 2008, 22:55
1
KUDOS
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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Current Student
Joined: 11 May 2008
Posts: 556
Re: GMATPrep - Square root question [#permalink]

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06 Aug 2008, 02:56
1
KUDOS
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
Retired Moderator
Joined: 18 Jul 2008
Posts: 970
Re: GMATPrep - Square root question [#permalink]

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06 Aug 2008, 17:23
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.
Senior Manager
Joined: 13 Dec 2009
Posts: 262
Re: GMATPrep - Square root question [#permalink]

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11 Mar 2010, 02:40
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

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Senior Manager
Joined: 01 Feb 2010
Posts: 264
Re: GMATPrep - Square root question [#permalink]

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12 Mar 2010, 09:38
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
Senior Manager
Joined: 01 Feb 2010
Posts: 264
Re: GMATPrep - Square root question [#permalink]

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12 Mar 2010, 09:42
1
KUDOS
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, 09:42
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