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

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Senior Manager
Joined: 14 Jun 2007
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1/(2+ sqrt(3)) = sqrt(3) - 2 2 - sqrt(3) sqrt(2) + [#permalink]  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
Manager
Joined: 15 Jul 2005
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Ans: 2-sqrt(3)

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

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

= 2 - sqrt(3)
Manager
Joined: 27 May 2007
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Re: PS Roots [#permalink]  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.
Senior Manager
Joined: 14 Jun 2007
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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?
GMAT Club Legend
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B. Solve by multiplying the fraction with 2-sqrt(3)/2-sqrt(3).
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