In exponentiation we have terms:
$$\text{base}^\text{exponent} = \text{power}.$$
But how the terms are called when dealing with the $n$-th root? For example:
$$\sqrt[n]{x} = z. $$
What are the names of the $n$, $x$, and $z$ terms in this expression?
If there are multiple names, please mention them all if possible.
Best Answer
In the expression $\sqrt[n]{x} = z$:
Generally speaking, the term $z$ is an $n$-th root of $x$. The expression itself will typically be defined in context such that it has a unique value, e.g. we will write $\sqrt[3]{8} = 2$ (and not, for example, $-1+i\sqrt{3}$, which also cubes to $8$). The notation might also indicate the principal $n$-th root of $x$. When $n=2$, we typically simplify the notation and write $$ \sqrt{x} = z. $$ In this case, $z$ is called the (principal) square root of $x$. When $x=1$, $z$ is a (principal) root of unity, e.g. $$ \sqrt[n]{1} = \text{the principal $n$-th root of unity}. $$ Roots of unity play a special role in a branch of math called "complex analysis." One might also see $z$ referred to as a surd.
The term $x$ is the radicand. Alternatively, if we regard $\sqrt[n]{\cdot}$ a a function, we might refer to $x$ as the argument of that function or, perhaps, the argument of the radical expression.
Most often, the $n$ is called the index of the radical. It may also be referred to as the degree. I have not seen this term in the wild, but a quick search of the interwebs indicates that this is not an uncommon terminology.
As long as we are giving names to things, the symbol $\sqrt{}$ is called the radical or surd, and the horizontal line over the radicand is called a vinculum. Note that nearly any horizontal bar in mathematics may be called a vinculum (e.g. the horizontal bar in the fraction $\frac{1}{2}$ is also a vinculum).