if 0*0=0, why can’t you divide 0 by 0 (the square root of 0) and get 0 (the square root of 0)?

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ditto for cube root, nth root, etc.

In: 5

13 Answers

Anonymous 0 Comments

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.

Anonymous 0 Comments

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?

————

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.

Anonymous 0 Comments

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.

Anonymous 0 Comments

By your logic, since 0 * 10 = 0, we could say that 0/0 = 10.

That’s the problem with 0/0 – it’s undefined, because you could make it equal whatever you want.

Anonymous 0 Comments

We want things to have a single definitive correct answer, so I can say:

x + 2 = 4

and the only right answer for “x” is “2”. “4 – 2 = 2”, that’s it, that’s the answer. We know because we can plug it back in as “x” and get the right result.

But while 0*0=0, we also have 0*1=0 and 0*2=0 and 0*1234567890=0.

So there’s no way to have a single right answer for 0/0, because when we get to “x * 0 = 0”,
any value can be plugged in for “x” and we get the right result.

Anonymous 0 Comments

Think of multiplication as “taking from a box of apples” and division as “putting into a box of apples”.

Using those definitions, “0 * [any number]” is the same as “taking 0 apples from the box [any number] times”. At the end, how many apples do you have? Zero because you never actually took anything from the box.

For division, “[any number] divided by zero” is the same as “how many times can you put 0 apples into the box if you start with [any number]”. It’s obviously a pointless exercise so they call it “undefined”.

Anonymous 0 Comments

Think of the plot of [y=1/x](https://upload.wikimedia.org/wikipedia/commons/4/43/Hyperbola_one_over_x.svg), compared to [y=x^2](https://study.com/cimages/multimages/16/2f02bcfd-854d-486a-ab39-30961b3337c4_yx2.jpg)

Anonymous 0 Comments

When we talk about dividing, what we are really doing is multiplying by the inverse. By that I mean that 7/9 is shorthand for 7*(1/9). So when you ask why we cannot divide by 0, you are really asking why 1/0 isn’t defined.

The reason 1/0 isn’t defined is because imagine 1/0=x. Then multiple both sides by 0 to get 1=x*0. However anything times 0 is 0, so we get 1=0, which is clearly wrong. Therefore 1/0 must be undefined.

Anonymous 0 Comments

Several people already explained how 0/0 can be literally any number, but I just want to chime in that for any number besides 0, x/0 is called “undefined” because an answer does not exist. On the other hand, 0/0 is called “indeterminate,” because there are infinite answers.

Anonymous 0 Comments

If we have to pick a number for 0/0, then it should be 1. Because for any other real number x/x = 1. So if you use lim x->0 (x/x), if you approach from both side, you will get 1.

It’s also why 0^0 is usually consider as 1.