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(1) a - b = √100 This means that a-b is +ve. For GMAT sqrt of something can not be -ve. So, a-b=10 ((a-b)^2)+4ab = (a+b)^2 = 100-36 = 64 (a+b) = 8 or -8 Not Enough. 2) Enough

(a +b) = sqrt (64) ---> Does GMAT considers -ve value of sqrt ?

If not, then answer could be D.

Hi, GMAT does not consider -ive value of square root , that is \(\sqrt{64}=8\).. But \((a + b)^2 = 64\) means a+b=8 or a+b=-8 and if it is given \((a +b) =(\sqrt{64}) = 8\).. these are two different things
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(a +b) = sqrt (64) ---> Does GMAT considers -ve value of sqrt ?

If not, then answer could be D.

Here is the reason the square root is always positive but a square considers both positive and negative value.

A positive number has two square roots: a positive square root (also called principal square root) and a negative square root. They are depicted as \(\sqrt{x}\) and \(-\sqrt{x}\). So by convention, \(\sqrt{x}\) implies we are talking about only the positive square root. Hence when you are given \(\sqrt{x}\) in the question, it implies that this is the principal square root only.

On the other hand, \(x^2 = 4\) has two solutions: x = 2 or -2 since x could take either of these values.
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