What is the remainder of an n-th root called?

Question

I feel like there should be a better word than remainder, but I don't know it. What do you call the thing that's left over when performing an $n$-th root? For example, $\sqrt[3]{29}$ is $3$ with 2 left over, while $\sqrt[3]{63}$ is also 3, but with $36$ left over. Is there a preferred notation for this quantity?

Answer 1

Let your wanted function be $r_n(a)$. If $a\ge 0$, then (in your case $n=3,a\in\{29,63\}$):

$$r_n(a)=a-\lfloor \sqrt[n]{a}\rfloor^n$$

Here I've used the floor function: $\lfloor x\rfloor$ is defined as the largest integer less than or equal to $x$.