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Crazy Roots

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CIO
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Crazy Roots [#permalink] New post 05 Jul 2007, 04:45
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 [#permalink] New post 05 Jul 2007, 05:13
(3(135^1/2) + 9/(4+15^1/2))^1/2

(9(15^2) + 9(4-15^1/2))^1/2
(36)^1/2
6
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 [#permalink] New post 05 Jul 2007, 05:46
I can simplify
(3(135^(1/2)) + (9/(4+5^(1/2))))^(1/2) to
(3*9(15^(1/2)) + (9/(4+5^(1/2)))^(1/2)

but how do you come up with

(9(15^2) + 9(4-15^1/2))^1/2) ?
Director
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 [#permalink] New post 05 Jul 2007, 06:13
9/4+sqrt15 can be written as (9/4+sqrt15)(4-sqrt15/4-sqrt15)) = 36-9sqrt15
3sqrt135 = 3sqrt(9*15)= 9sqrt(15)

therefore the given question leads to sqrt(9sqrt15+36-9sqrt15) = 6

Answer is 6
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 [#permalink] New post 05 Jul 2007, 06:49
=sqrt ( 3 sqrt (15 x 9) + 9/4 + sqrt15)
= sqrt (((9 sqrt15) x (4 + sqrt15) +9)/ 4+ sqrt15)
= sqrt (( 36 sqrt15 +135+ 9)/ 4 + sqrt15)
= sqrt (36 sqrt15 + 144/ 4 + sqrt15)
= sqrt (36 (4 + sqrt15)/ 4 + sqrt15)
= sqrt 36
= 6
Hence, B.
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 [#permalink] New post 05 Jul 2007, 07:38
Thanks for the explanation, I'm horrible at re-writing equations. :wall
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 [#permalink] New post 07 Jul 2007, 08:56
OA is 6. Nice job everyone.
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 [#permalink] New post 07 Jul 2007, 09:08
ian7777 wrote:
OA is 6. Nice job everyone.


Nice problem ian7777 , thanks.

:-D
  [#permalink] 07 Jul 2007, 09:08
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