We called them surds in the Dark Ages.

gg5: 〘数〙 a surd; an irrational （number）.
koj and daijisen also.

https://en.wikipedia.org/wiki/Nth_root
> An unresolved root, especially one using the radical symbol, is sometimes referred to as a surd or a radical.

Google N-gram Corpus Counts
╭─ーーーーーーー─┬───────╮
│ 根数　　　　　 │ 1,248 │
│ 不尽根数　　　 │     0 │
│ ふじんこんすう │     0 │
╰─ーーーーーーー─┴───────╯

This seems to be more specific than "irrational number"

@@ -13 +13,2 @@
-<gloss>irrational number</gloss>
+<gloss>surd</gloss>
+<gloss>irrational root</gloss>

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