is there such thing as a pentagon root like theres a square root?

Question

amistre64 · Answer

numbers used to be proved by geometry.  not sure if they needed a pentagon root perse

osanseviero · Answer

A square root is like doing:
$$x ^{1/2}$$

And yes, you could use five, but it is called fifth root.
You can use any number, really.

It is named square root because, when you square a number, you are finding the area of a square.

empty · Answer

yeah but a pentagon root would not be the same as a fifth root. Just like the cube root is not a triangle root you know?

alexandervonhumboldt2 · Answer

i think there can be such roots

osanseviero · Answer

If you do x^2, you are working with a square (2 dimensions)
If you do x^3, you are working with a cube (3 dimensions).
After 3 we work with fourth, fifth, and so on. It is not the number of sides of the figure

empty · Answer

right, that's why I said the triangle root is not the same as a cube root.

osanseviero · Answer

Do triangle roots exist?

empty · Answer

thats what I'm asking

osanseviero · Answer

They exist, but in another context.

empty · Answer

yeah I know, so stop thinking in your context and think in my contxt haha

osanseviero · Answer

Based on google:

In analogy to the square root of x, one can calculate the heptagonal root of x, meaning the number of terms in the sequence up to and including x.

There is also triangular roots and more, but they don't have the same meaning. First we should check what a triangular or heptagonal numbers are.

perl · Answer

you would have to define it carefully.
A square root of x is the side of a square which has area x.
What would be the pentagonal root. a side of a pentagon with area x ?

perl · Answer

a cube root of x is the side of a cube which has volume x .