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The square root of $n$ is $n^{1/2}$

The cube root of $n$ is $n^{1/3}$

Is there a term for $n^{1/4}$

Or would you just say 4th root or something?

Update:

I'm asking if there's a term for this root, or if they're only labeled up to the cube (probably because the terms make an analogy to shapes, and we humans can only conceptualize up to 3 dimensions)..

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There isn't a standard term other than fourth root. –  Jim Mar 25 '13 at 17:05
    
you could try with square root of a square root, but in this way you will stuck at the next $1/5$ –  user67878 Mar 25 '13 at 17:07

4 Answers 4

up vote 4 down vote accepted

Wikipedia mentions the following on roots:

A root of degree 2 is called a square root and a root of degree 3, a cube root. Roots of higher degree are referred to using ordinal numbers, as in fourth root, twentieth root, etc.

While the "tesseract root" might make sense, it is probably not a widely recognized term for the fourth root.

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Since fourth degree polynomials are called quartic polynomials and the formula for their solution is usually called the quartic formula, I have usually heard "fourth root" or "quartic root" for $\sqrt[4]{x}=x^{1/4}$.

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In really old literature (before 1900), a fairly standard term for the 4th root is biquadratic root. See this 1800-1899 google-books search for "biquadratic root".

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you could say 4th root, I suppose if you want to keep the flow going you could either say:

Tesseract root? (4-d cube/square)

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5  
If you say Tesseract root no one will know what you're talking about. –  Jim Mar 25 '13 at 17:04
    
Its not meant to make a serious answer haha... it just seemed the asker was curious what would the next word be? –  frogeyedpeas Mar 25 '13 at 17:11
    
A Tesseract root reminds me of that book A Wrinkle in Time –  Mike Christensen Mar 25 '13 at 17:16

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