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Square roots

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Senior Manager
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Square roots [#permalink] New post 03 Oct 2008, 11:06
Please solve
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Director
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Joined: 27 Jun 2008
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WE 1: Investment Banking - 6yrs
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Re: Square roots [#permalink] New post 03 Oct 2008, 11:29
D

I must confess, it took me a while to solve this, however, if its a "GMAT" problem, you should be able to solve it within 2 mins. So, I was rattling my brian.

Anyway, rt63 = 3rt7.

> ROOT 2rt63 + 2 / 8+rt63
> ROOT 8*2rt63 + rt63*rt63*2 + 2 / 8+rt63
> ROOT 16rt63 + 128 / 8+rt63
> ROOT 16(rt63 + 8) / (8 + rt63)
> ROOT 16 = 4
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Re: Square roots [#permalink] New post 03 Oct 2008, 11:36
we know that 8+sqrt(63)/8+sqrt(63) = 1

so:

sqrt(2sqrt(63)+2/8+3*sqrt(7)) = x

2*sqrt(63)+2/8+3*sqrt(7) = x^2

2*sqrt(63)*1+2/8+sqrt(63) = x^2

2*sqrt(63)*(8+sqrt(63)/8+sqrt(63))+2/8+sqrt(63) = x^2

(2*sqrt(63)*(8+sqrt(63))+2)/8+sqrt(63) = x^2

(16*sqrt(63)+63*2+2)/8+sqrt(63) = x^2

16*sqrt(63)+128/8+sqrt(63) = x^2

16*(sqrt(63)+8)/(8+sqrt(63)) = x^2

16*1 = x^2

x = 4

:)

The answer is (D)
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Re: Square roots [#permalink] New post 06 Oct 2008, 01:42
Answer is D.

And the calculation was even not that complex. You can solve it directly. :-D
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Re: Square roots [#permalink] New post 06 Oct 2008, 02:01
vksunder wrote:
Please solve


if GMAT is for business leaders , i will think like one and use approximation

sqrt(2sqrt63 + 2 / 8+3sqrt7)

sqrt 63 = approximately sqrt 64 = 8

sqrt 7 approx = sqrt 9 = 3

sqrt ( 2*8 + 2 / 3*3) = sqrt (16 + 2 /17) = sqrt ( 274/ 16) = sqrt 274 / sqrt 16 =

approx sqrt ( 16^2) / sqrt 16 = 16/4 = 4
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Re: Square roots [#permalink] New post 06 Oct 2008, 05:05
Very Good point yezz. Damn, I need to start thinking like a leader:)
Re: Square roots   [#permalink] 06 Oct 2008, 05:05
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