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    • Thread Starter

    I'm curious as to why a square root normally has two solutions (a negative and positive solution) but a cubic root only has 1 solution. Could anyone help me out? =]

    If you think of an example :

    if x is -2 then (-2)sqquared is 4.. ( 2 minus cancell eachother out )
    if x is +2 then (+2)squared is also 4..

    when its cubed

    if x is (-2) then x squared is 4, but then times (-2) again so the minus comes back.
    if x is posstive then x squared is 4, but then times 2 again it is just 8 (no negatives)

    Pretty crap explantion, but might help=/
    • Thread Starter

    ahhh i see.

    I was more trying to figure it out the other way lol. I think i got it now though thanks.

    When you cube root say 27 it can can only be 3 (as only +3 x +3 x +3 = +27). Whereas when you cube root -27 it can only be -3 (dispite my calculator disagreeing with me cube rooting negatives)?
    • Thread Starter

    scratch that my calculator does cube root negatives! lol :woo:

    You've asked a really good question!

    You're happy that 1 has two square roots - +1 and -1.

    How many square roots does -1 have? Until you meet complex numbers the answer is 'you can't take the square root of a negative number' or 'my calculator says ERR'. Then at A level you meet the square root of -1 and give it a name: i. So -1 has two square roots i and -i.

    Turns out that once you allow complex numbers, 1 has three cube roots. So you were right!
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Updated: January 17, 2010
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