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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] New post 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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 [#permalink] New post 06 Dec 2003, 15:58
First term is positive, second term is negative, third term is positive.

Only one negative answer.

D
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 [#permalink] New post 06 Dec 2003, 16:01
stoolfi wrote:
First term is positive, second term is negative, third term is positive.

Only one negative answer.

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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 [#permalink] New post 06 Dec 2003, 16:06
can only be -ve. and we have only one choice that concurs.

:)
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 [#permalink] New post 07 Dec 2003, 06:37
dj wrote:
praetorian123 wrote:
stoolfi wrote:
First term is positive, second term is negative, third term is positive.

Only one negative answer.

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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AkamaiBrah
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 [#permalink] New post 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
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 [#permalink] New post 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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 [#permalink] New post 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
  [#permalink] 15 Dec 2003, 20:28
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