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sqrt(4) = 2 which is our above value of x multiplied by -1; hence the answer is -x.

[/quote]

Using this exact same method, what keeps us from getting sqrt(4) = -2? This would give us "x" or answer [D]. How do we know not to let sqrt(4) = +/-2 in certain problems?
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"The price of anything is the amount of life you exchange for it." -Thoreau

Can someone please explain to me again why square root of 4 cannot be -2 as well as 2? Is it the square root of a number always have two roots, one positive and one negative?

Can someone please explain to me again why square root of 4 cannot be -2 as well as 2? Is it the square root of a number always have two roots, one positive and one negative?

Yea, I'm still waiting on this clarification as well.
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"The price of anything is the amount of life you exchange for it." -Thoreau

Can someone please explain to me again why square root of 4 cannot be -2 as well as 2? Is it the square root of a number always have two roots, one positive and one negative?

True, by definition, square roots have a positive and negative value, but the GMAT only recognizes the positive root of a number. Example: root4 = +2 (not -2)

However, if you are squaring a variable, the value for that variable will be a positive and negative value Example: x^2 = 4 --> x = +/-2

Just something to keep in mind on test day!!
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Factorials were someone's attempt to make math look exciting!!!