what is the zeroth root of any number ?

Answer 1

Several answerers are getting confused by zeroth power and zeroth root. Anything to the zeroth *power* is 1, but anything to the zeroth *root* is undefined.

Here's one way to think of it:

We agree that x^0 = 1 (for any nonzero x). Therefore only 1 could possibly have a zeroth root. But, again, which x are we going to use? This means that the zeroth root of 1 is indeterminate. It would be written as 1^(1/0) but that is obviously undefined.

Another way to think of this is to think about the sequence of roots:

Cube root = x^(1/3)
Square root = x^(1/2)
"First" root = x^(1/1)
"Zeroth" root = x^(1/0)

So again, you can see that this would be undefined or indeterminate.

Answer 2

You want to solve X^0 = N for known N and unknown X.

X = 0 is no good. Substituting, we get 0^0 = N. 0^0 is undefined, but not completely undefined. It usually turns out to be either 1 or 0, depending on how you arrived at each zero. So if N = 1 or N = 0, then its zeroth root could be 0, but it might not be.

X = infinity is good. Substituting, we get infinity^0 = N. infinity^0 is completely undefined, so we have a perfectly good equation. The left-hand side can be anything, including N, even when N = 0 or N = 1.

Answer 3

if the number >1 then the zeroth root is infinity
if the number <1 then the zeroth root is 0
if the number =1 then it is undefined

Answer 4

the zeroth root of 0 is 0 and for any other no is infinity

Answer 5

1

Answer 6

zeroth root of any number is when >1 =infinity and when <1=0
when =1 is undefined

Answer 7

the zeroth root is DEFINED to be an identity operation

in the same way that X * 1 = X or
X + 0 = X

X ^ 0 = X

Answer 8

Undefined

Answer 9

Undefined. This comes from the definition of root.

Answer 10

Infinity