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which of the following is equal to ^2 a)1 b)5 c) 6^(1/2) d)

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which of the following is equal to ^2 a)1 b)5 c) 6^(1/2) d) [#permalink] New post 15 May 2008, 10:35
which of the following is equal to [1/((3^1/2)-(2^1/2))]^2

a)1
b)5
c) 6^(1/2)
d) 5 - 6^(1/2)
e) 5+ 2* (6)^(1/2)
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Re: sqrt [#permalink] New post 16 May 2008, 01:48
Hello,

Response is E.
How? :
We have [(3^1/2 - 2^1/2)]^2 = 3+2-2*6^1/2=5-2*6^1/2
We also know that (5+2*6^1/2) * (5-2*6^1/2)=5^2-(2*6^1/2)^2=25-24=1
Which leads to 1/[5-2*6^1/2] = [(5+2*6^1/2)*(5-2*6^1/2)]/(5-2*6^1/2) = 5+2*6^1/2
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Re: sqrt [#permalink] New post 16 May 2008, 02:35
puma wrote:
which of the following is equal to [1/((3^1/2)-(2^1/2))]^2

a)1
b)5
c) 6^(1/2)
d) 5 - 6^(1/2)
e) 5+ 2* (6)^(1/2)


E it is. Simple strategy for such kinds...
Simplify the denominator first by a^2 - b^2 rule. So multiply both numerator and denominator by ((3^1/2)+(2^1/2)).
This will make denominator as 1 (a=3^1/2 and b=2^1/2).
Now the problem equation is [((3^1/2)+(2^1/2))]^2 = 3 + 2 + 2*(3)^1/2*(2)^1/2 = 5+2*(6)^1/2
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Re: sqrt [#permalink] New post 16 May 2008, 06:51
puma wrote:
which of the following is equal to [1/((3^1/2)-(2^1/2))]^2

a)1
b)5
c) 6^(1/2)
d) 5 - 6^(1/2)
e) 5+ 2* (6)^(1/2)


There is a very easy way to solve this. The approaches above are very good as well.

sqrt3= 1.7
sqrt2= 1.4

1/.3 = 10/3 =3.333333

Now check the answers. we know that 3^2=9, thus 3.3333^2>9

All besides E are less than or equal to 5. so E it is.
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Re: sqrt [#permalink] New post 16 May 2008, 07:10
i get E as well..

5+2*sqrt(6)

basically multiply the whole thing by {sqrt(3)+sqrt(2)}/{sqrt(3)+sqrt(2)}
Re: sqrt   [#permalink] 16 May 2008, 07:10
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which of the following is equal to ^2 a)1 b)5 c) 6^(1/2) d)

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