# How do you express any radical root of a number?

I'm writing a reference for my piece of code, and one of the sentences is bugging me. The line I'm trying to express is something like:

The value is raised to the power of the reciprocal of x.

Did you get that I was trying to mean radical root on the first try (for example, if x = 2, the value will be square-rooted?) I think this line is little too complex for some people to read. I'm writing a document that can possibly be read by anyone (even people whose mother tongue isn't English,) so I want to be as clear as possible.

The sentence would be simpler if there were an expression I can use to represent any radical root. just as simple as `2^5` expressed as

2 to the power of 5

However, I haven't been able to find any. Are there any, or do I have to stick with "to the power of?"

• We usually include the suffix -th for clarity, so most commonly it's the nth root. Since the xth root would be a bit of a mouthful, that would probably usually be written as the x root, but I bet many writers would simply change their example context to use n rather than x. – FumbleFingers Reinstate Monica Jan 8 '17 at 15:57
• @FumbleFingers "x-th" is no more of a mouthful than "sixth", you might find the /s/ gets dropped in speech and it'll be pronounced /ekθ/ or /sɪkθ/ Then again, you might not. – Au101 Jan 8 '17 at 21:12
• @Au101: I kinda doubt many native speakers actually enunciate the /s/, but that's not much of a problem with SIKTH because we hear and say it enough so people get used to it. But EKTH just sounds a bit weird, and I at least feel a stronger urge to attempt the full enunciation even though my mouth isn't really up to the job. – FumbleFingers Reinstate Monica Jan 9 '17 at 13:45

If I understand you correctly, you are referring to the following equation: .... the inverse function of an

That being the case, in mathematics it is referred to as the nth root of a number, in this case the number being a.

In spoken form, one would say (for the values of n given)

• (n=4) the fourth root of a
• (n=5) the fifth root of a
• (n=6) the sixth root of a
• (n=7) the seventh root of a

...and so on. There are two exceptions, when n=2 or n=3. Here we would say:

• (n=2) the square root of a
• (n=3) the cube root of a
• Yes, that's the right equation. One question - if x is not an integer (like 1.5, it can happen with my piece of code,) does it still make sense? – Collapsed PLUG Jan 8 '17 at 15:49
• Good question. If you're looking for an abstract term, then nth root should cover it. For example, if a sentence read '...and the answer is the nth root of 5, where n=1.5...', it seems perfectly acceptable to me at least. – mike Jan 8 '17 at 16:00

You have to say

The value is raised to the power of 1/x.

Or spoken aloud:

The value is raised to the power of one over x.

Mathematicians don't talk about "xth roots" when x is not an integer.

For positive integers n, "nth root" (pronounced "enth root") is fine.