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# The value of (4+sqrt15) * (sqrt6-sqrt10) * sqrt(4-sqrt15) is

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The value of (4+sqrt15) * (sqrt6-sqrt10) * sqrt(4-sqrt15) is [#permalink]

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06 Dec 2003, 15:41
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3. The value of (4+sqrt15) * (sqrt6-sqrt10) * sqrt(4-sqrt15) is

a. 1
b. 0
c. 2
d. -2
e sqrt(15)

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06 Dec 2003, 15:58
First term is positive, second term is negative, third term is positive.

D
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06 Dec 2003, 16:01
stoolfi wrote:
First term is positive, second term is negative, third term is positive.

D

you think like me . that's a gmat solution right there.

what if all the choices were negative. ..just for the sake of discussion
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06 Dec 2003, 16:06
can only be -ve. and we have only one choice that concurs.

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07 Dec 2003, 06:37
dj wrote:
praetorian123 wrote:
stoolfi wrote:
First term is positive, second term is negative, third term is positive.

D

you think like me . that's a gmat solution right there.

what if all the choices were negative. ..just for the sake of discussion

2

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Best,

AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

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07 Dec 2003, 06:51
akamai, i have a question:

Did the others, including me ignore the negative value of the sqrt root here?

Example

4 + sqrt (16) ....this would be 8 isnt it?

but sqrt(16) = - 4 too...

Do we always take the positive value of the sqrt root in "expressions", unless otherwise mentioned.

thanks
praetorian
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07 Dec 2003, 07:11
praetorian123 wrote:
akamai, i have a question:

Did the others, including me ignore the negative value of the sqrt root here?

Example

4 + sqrt (16) ....this would be 8 isnt it?

but sqrt(16) = - 4 too...

Do we always take the positive value of the sqrt root in "expressions", unless otherwise mentioned.

thanks
praetorian

In the gmat, the square root sign signifies positive square root. HOWEVER, since I squared an expression in one of the steps in my solution, I no longer can claim the square root to be positive, i.e., I cannot say if x = -2 I cannot say since x^2 = 4, x = sqrt(x^2) = 2.

Going back to my solution, I would have to notice that the answer must be negative, then choose the correct root.
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AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

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15 Dec 2003, 20:28
The value of (4+sqrt15) * (sqrt6-sqrt10) * sqrt(4-sqrt15) = x
x * sqrt(4-sqrt15) = (4+sqrt15) * (sqrt6-sqrt10) * (4-sqrt15)
= (16-15) * ( sqrt6-sqrt10 )

now squaring both sides we get
sqr(x) * ( 4-sqrt15 ) = 6+10-2 * sqr(6*10)

sqr(x) * ( 4-sqrt15 ) = 16-4 * sqrt(15)
sqr(x) * (4-sqrt15 ) = 4(4-sqrt(15))

sqr(x) = 4 so x = +-2
x cannot be +ve because sqrt(4-sqrt15) is +ve and
(sqrt6-sqrt10) is -ve. Just from this we should be able to conclude that the answer is -ve
15 Dec 2003, 20:28
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