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Here's the question I've been thinking for $2$ days and couldn't find an answer why.

If $Y = \sqrt{X}$, where both $X$ and $Y$ are real numbers then which of the following is true?

a) $X\geq 0$; $Y\geq 0$

b) $X\leq 0$; $Y\geq 0$

c) $X\leq 0$; $Y\leq 0$

d) $X\geq 0$; $Y\leq 0$

e) Either a) or b)

Now, the answer is a) but I don't know why. I know a value of $Y$ for which root of $Y$ is negative.

$\sqrt{4} = \pm2$

$\sqrt{9} = \pm3$

So the answer should be $X\leq0$; $Y\geq0$, but its not. :(

Can anyone explain me why? Thanks in advance. :)

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    OMG, GEEK TALK! :D2010-08-30

1 Answers 1

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As has been indicated in the comments, the radical symbol is generally taken to be the principal square root function, which for nonnegative real inputs gives nonnegative real outputs. For negative real inputs, this function gives non-real outputs, so X must be nonnegative, so Y must be nonnegative, giving (a).