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1/(2+ sqrt(3)) = sqrt(3) - 2 2 - sqrt(3) sqrt(2) +

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Senior Manager
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1/(2+ sqrt(3)) = sqrt(3) - 2 2 - sqrt(3) sqrt(2) + [#permalink] New post 08 Jul 2007, 12:53
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1/(2+ sqrt(3)) =


sqrt(3) - 2
2 - sqrt(3)
sqrt(2) + sqrt(3)
2 + sqrt(3)
sqrt(3) + 4
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 [#permalink] New post 08 Jul 2007, 12:58
Ans: 2-sqrt(3)


1/(2+sqrt(3)) : multiply and divide by (2-sqrt(3))

(2-sqrt(3)) / 4 - 3

= 2 - sqrt(3)
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Re: PS Roots [#permalink] New post 08 Jul 2007, 14:08
anonymousegmat wrote:
1/(2+ sqrt(3)) =


sqrt(3) - 2
2 - sqrt(3)
sqrt(2) + sqrt(3)
2 + sqrt(3)
sqrt(3) + 4


If you don't know how to solve for this algebraically, try ballparking. It's good to know that the sq rt of 3 is @1.7. 1/(2+1.7) is 1/3.7, or less than 1/3. Ans 1 is 1.7 - 2, a negative #, so rule it out. Ans 2 is 2 - 1.7, or .3, which is less than 1/3 (the right answer). If you plug is 1.7 for sqrt3 in the other possible solutions, you will see that they are out of the ballpark.
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 [#permalink] New post 08 Jul 2007, 15:42
chets wrote:
Ans: 2-sqrt(3)


1/(2+sqrt(3)) : multiply and divide by (2-sqrt(3))

(2-sqrt(3)) / 4 - 3

= 2 - sqrt(3)


chet,

how did you know to multiply by 2-sqroot3/2-sqroot3?
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 [#permalink] New post 08 Jul 2007, 17:04
B. Solve by multiplying the fraction with 2-sqrt(3)/2-sqrt(3).
  [#permalink] 08 Jul 2007, 17:04
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