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Sq. root (Real Number)

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Sq. root (Real Number)

by euro » Sat Oct 30, 2010 5:47 am
Image

Please refer to the problem attached as an image.

Question:
Should we assume that only positive values will result from a square root?
For instance, if we assume x = 1, then Sq root (x) = sq. root (1) = +1 or -1.
In this case, the correct answer to the above problem could be (A) also.

Please provide some insights.
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by GMATGuruNY » Sat Oct 30, 2010 6:18 am
euro wrote:Image

Please refer to the problem attached as an image.

Question:
Should we assume that only positive values will result from a square root?
For instance, if we assume x = 1, then Sq root (x) = sq. root (1) = +1 or -1.
In this case, the correct answer to the above problem could be (A) also.

Please provide some insights.
When the GMAT writers use the square root symbol √, they mean the positive root only.

√4 = 2.
√9 = 3.
√x means the positive square root of x.

However, we when we solve by taking the square root, we have to account for the both the positive and negative roots:

x^2 = 16
x = 4 or -4.

Clear?
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by shovan85 » Sat Oct 30, 2010 6:26 am
euro wrote:Image

Please refer to the problem attached as an image.

Question:
Should we assume that only positive values will result from a square root?
For instance, if we assume x = 1, then Sq root (x) = sq. root (1) = +1 or -1.
In this case, the correct answer to the above problem could be (A) also.

Please provide some insights.
I think if you have to choose a side. If u are taking -ve part then u have to consider all -ve parts. Doing so u will have a real answer if u choose -ve 1.
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by euro » Sat Oct 30, 2010 6:32 am
This was a secret to me up until now.

So, just to rephrase what you explained: if we (test-takers) perform a square root operation during any of our calculations, then we have to assume both +ve and -ve values; if GMAT uses a *square root sign* in one of its problems, then we have to consider ONLY the +ve values resulting from such a square root.
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by shovan85 » Sat Oct 30, 2010 6:40 am
euro wrote:This was a secret to me up until now.

So, just to rephrase what you explained: if we (test-takers) perform a square root operation during any of our calculations, then we have to assume both +ve and -ve values; if GMAT uses a *square root sign* in one of its problems, then we have to consider ONLY the +ve values resulting from such a square root.
Its what I think but they can play around with are thought process so when confused in areas like this pick the concrete one. I will show you an example of over thinking. Just trust yourself :)

https://www.beatthegmat.com/gmat-prep-no ... 68879.html
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by GMATGuruNY » Sat Oct 30, 2010 7:19 am
euro wrote:This was a secret to me up until now.

So, just to rephrase what you explained: if we (test-takers) perform a square root operation during any of our calculations, then we have to assume both +ve and -ve values; if GMAT uses a *square root sign* in one of its problems, then we have to consider ONLY the +ve values resulting from such a square root.
Correct!
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My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

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