ditto for cube root, nth root, etc.
In: 5
When you are asking “what is *a* divided by *b*”, what you’re really asking is “What number, when multiplied by *b*, equals *a*?”
In this case, what number, when multiplied by 0, equals 0? And the answer is, every number. And that’s why the answer is undefined, because it doesn’t give a concrete answer.
So if we want…
> 0 / sqrt(0) = sqrt(0)
But we would also get:
> 0 * (1/sqrt(0)) = 0
as anything multiplied by 0 is 0.
But also, if sqrt(0) = 0, we get:
> 0 / sqrt(0) = 0 / 0 = 1
as anything divided by itself is 1.
And, of course, we get:
> 0 / sqrt(0) = [something] / 0 = ….?
as you cannot divide by 0.
So which is it? Is this sqrt(0), 0, 1 or undefined?
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So sure, if we “divide both sides by sqrt(0)” we get:
> 0 * sqrt(0) = sqrt(0)
which is a valid statement.
The problem with extrapolating this is that
> 1 * sqrt(0) = sqrt(0)
as well. And also:
> 20 * sqrt(0) = sqrt(0)
so if we try to divide, we get:
> sqrt(0)/sqrt(0) = 1 = 20 = 0
which doesn’t work.
because anything*0=0, so 0/0 is “anything”, i.e. literally could be any number.
0 is square root of 0, no controversy there.
square roots do not change the issue with division.
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