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Thread: Brain fart on square roots

  1. #1
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    Brain fart on square roots

    √9 = 3
    but is it also - 3?

    how do i know when a square root is + or -?
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    Quote Originally Posted by NeedHelp18 View Post
    √9 = 3
    but is it also - 3?

    how do i know when a square root is + or -?
    $\displaystyle \sqrt{9}=3$. I don't think it can be negative. I mean, if it was $\displaystyle -\sqrt{9}$, then it would equal $\displaystyle -3$. But I really don't think it would be negative....i'm not too sure though.
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  3. #3
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    Quote Originally Posted by NeedHelp18 View Post
    √9 = 3
    but is it also - 3?

    how do i know when a square root is + or -?
    Hello,

    Indeed, $\displaystyle \sqrt{\dots}$ is always positive (in higher grades it may not, but it's another story )

    There is a hesitation to have when you get :

    x=9

    Here, x is either 3 either -3. Why ?

    x=9 <=> x-9=0 <=> (x-3)(x+3)=0

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    Quote Originally Posted by Moo View Post
    Hello,

    Indeed, $\displaystyle \sqrt{\dots}$ is always positive (in higher grades it may not, but it's another story )

    There is a hesitation to have when you get :

    x=9

    Here, x is either 3 either -3. Why ?

    x=9 <=> x-9=0 <=> (x-3)(x+3)=0

    Yes, yes indeed!

    Then there are imaginary numbers too! like:$\displaystyle \sqrt{-x}=i\sqrt{x}$ ....but who needs to learn that now? ...sorry if i'm confusing you...
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    Quote Originally Posted by Moo View Post
    Indeed, $\displaystyle \sqrt{\dots}$ is always positive
    $\displaystyle \sqrt 0 = 0$ Are they always positive?
    How about non-negative!
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    Moo
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    Quote Originally Posted by Plato View Post
    $\displaystyle \sqrt 0 = 0$ Are they always positive?
    How about non-negative!
    Isn't 0 considered as a positive integer ? oO

    $\displaystyle 0 \in \mathbb{N}$

    Erm.. I'm lost
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    Quote Originally Posted by Moo View Post
    Isn't 0 considered as a positive integer ?
    Absolutely not!
    The real numbers are partitioned into three sets: {negatives}, {0}, & {positives}.

    Quote Originally Posted by Moo View Post
    $\displaystyle 0 \in \mathbb{N}$
    You are confusing two concepts.
    So authors insist that 0 is a counting number.
    Some say no it is a whole number but not a natural number.
    Others disagree with both of those.
    But that has nothing to do with 0 being positive. It is not.
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    Moo
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    Quote Originally Posted by Plato View Post
    Absolutely not!
    The real numbers are partitioned into three sets: {negatives}, {0}, & {positives}.


    You are confusing two concepts.
    So authors insist that 0 is a counting number.
    Some say no it is a whole number but not a natural number.
    Others disagree with both of those.
    But that has nothing to do with 0 being positive. It is not.
    Oh I see...
    In the French wikipedia, it is said that 0 is a natural integer, not in the English one
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    Hi, NeedHelp18!

    All positive real numbers have two real square roots. However, the radical notation $\displaystyle \sqrt{a}$ generally refers only to the principal square root, which is always the nonnegative value. If you want to represent both square roots, use the notation $\displaystyle \pm\sqrt{a}$. This also applies to $\displaystyle \sqrt[n]{a},\text{ where }n\text{ is even}$. As others mentioned, things get more complicated when you bring complex values into consideration.

    And no, Moo, 0 is neither positive nor negative, but it may be included in the set of natural numbers depending on what definition you are using.
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