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# square and cubic root solutions watch

1. 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? =]
2. 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=/
3. 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)?
4. scratch that my calculator does cube root negatives! lol
5. 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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