A square root has two solutions.
It follows that a cube root has three solutions.
Is this correct?
.
Infinity free: square roots/cube roots
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Infinity free: square roots/cube roots
Last edited by C on 05 Jun 2018, 19:16, edited 1 time in total.
mudshark wrote:Where is he anyway, that very soft lad?
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Re: Infinity free: square roots/cube roots
*fires elastic band at C's head when his back is turned*
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Re: Infinity free: square roots/cube roots
If you mean in the sense that a square root has a negative as well as a positive solution, then no.
negative x negative x negative = negative
negative x negative x negative = negative
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Re: Infinity free: square roots/cube roots
Harvey K-Tel wrote:*fires elastic band at C's head when his back is turned*
.
mudshark wrote:Where is he anyway, that very soft lad?
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Re: Infinity free: square roots/cube roots
Harvey K-Tel wrote:*fires elastic band at C's head when his back is turned*
You hit him low, I'll hit him high.
Don't fake the funk on a nasty dunk!
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Re: Infinity free: square roots/cube roots
The cube root of negative 8 is negative 2
ie
-2 x -2 x -2 = -8
One root. So incorrect?
.
ie
-2 x -2 x -2 = -8
One root. So incorrect?
.
mudshark wrote:Where is he anyway, that very soft lad?
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Re: Infinity free: square roots/cube roots
Pansy Puff wrote:Cube roots of -8 are -2, 1 + root(3)i and 1 - root(3)i
Where i is the square root of -1
So the square root of -4 is equal to square root of 4 multiplied by square root of -1 (can we do this? check with something you know - is the square root of 36 equal to square root of 4 multiplied by square root of 9...? Yes it is!)
= square root of 4 x i
so the two roots are 2i and -2i [called conjugate roots]
The process of square roots of negative numbers takes us away from real numbers into imaginary numbers or complex numbers
So, applying this allows us to solve cube roots.
All real numbers (except zero) have exactly one real cube root and a pair of complex conjugate cube roots
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Last edited by C on 07 Jun 2018, 16:55, edited 1 time in total.
mudshark wrote:Where is he anyway, that very soft lad?
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Re: Infinity free: square roots/cube roots
Good lad
True – and I agree. I was about to edit out ‘except zero’ when you replied.
Those that would include are only considering the end product 0 x i =0 and not the big 'open' picture.
It takes me back to my earlier point of 1=3/3 etc
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True – and I agree. I was about to edit out ‘except zero’ when you replied.
Those that would include are only considering the end product 0 x i =0 and not the big 'open' picture.
It takes me back to my earlier point of 1=3/3 etc
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Re: Infinity free: square roots/cube roots
*looks around for more elastic bands*
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Re: Infinity free: square roots/cube roots
C wrote:Pansy Puff wrote:Cube roots of -8 are -2, 1 + root(3)i and 1 - root(3)i
Where i is the square root of -1
So the square root of -4 is equal to square root of 4 multiplied by square root of -1 (can we do this? check with something you know - is the square root of 36 equal to square root of 4 multiplied by square root of 9...? Yes it is!)
= square root of 4 x i
so the two roots are 2i and -2i [called conjugate roots]
The process of square roots of negative numbers takes us away from real numbers into imaginary numbers or complex numbers
So, applying this allows us to solve cube roots.
All real numbers (except zero) have exactly one real cube root and a pair of complex conjugate cube roots
.
For some reason I find this rather pleasing.
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Get a fucking grip you narcissistic cretins.
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Re: Infinity free: square roots/cube roots
C wrote:A square root has two solutions.
It follows that a cube root has three solutions.
Is this correct?
.
Correct
.
mudshark wrote:Where is he anyway, that very soft lad?