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# The expresion SQRT(57-40*SQRT2) - SQRT(57+40*SQRT2) is equal

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CEO
Joined: 15 Aug 2003
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The expresion SQRT(57-40*SQRT2) - SQRT(57+40*SQRT2) is equal [#permalink]  06 Dec 2003, 14:59
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6. The expresion SQRT(57-40*SQRT2) - SQRT(57+40*SQRT2) is equal to :

a. 10 b. -10 c. 101/10 d.-101/10 e.-SQRT41
Director
Joined: 13 Nov 2003
Posts: 792
Location: BULGARIA
Followers: 1

Kudos [?]: 27 [0], given: 0

Raise the whole expression to power 2 and solve it. Think it should be 10..
Intern
Joined: 04 Oct 2003
Posts: 42
Location: Silicon Valley, CA
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Kudos [?]: 1 [0], given: 0

squaring the entire expression

if a = 57
and b = 40*2^1/2

a^2 + b^2 -2((a+b)(a-b))^1/2. siplyfiy to get 114-2(49)^1/2 = 100

Ans = 10
Senior Manager
Joined: 12 Oct 2003
Posts: 251
Location: USA
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Kudos [?]: 5 [0], given: 0

is bat_car's work correct?

How would you get a^2 + b^2 -2((a+b)(a-b))^1/2
shouldn't it be 2a -2((a+b)(a-b))^1/2

also the value of the squared expression comes to be 100

so taking its square root how do we get only 10. Shouldn't it be -10 as well??
SVP
Joined: 30 Oct 2003
Posts: 1797
Location: NewJersey USA
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Kudos [?]: 41 [0], given: 0

End result of whole expression squared is 100. SO sqrt of 100 either -10 or +10.
But if you see the orginal expression

SQRT(57-40*SQRT2) < SQRT(57+40*SQRT2)
SO the answer should be -10
Senior Manager
Joined: 11 Nov 2003
Posts: 355
Location: Illinois
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Kudos [?]: 0 [0], given: 0

I agree with Anand.

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