Is there a one-word term for "grows by square root"?

We can describe a growth relationship $$y = x$$ as linear (e.g. "linear growth").

We can describe $$y = \log(x)$$ as logarithmic (e.g. "logarithmic growth").

We can describe $$y = x^2$$ as quadratic (e.g. "quadratic growth").

We can describe $$y = 2^x$$ as exponential (e.g. "exponential growth").

Is there a one-word term to describe a growth relationship where $$y = \sqrt{x}$$ ?

The best suggestion I've seen is "radical growth", which does not seem to be a standard term and I think would cause confusion if used without explanation.

The asymptotic growth of a root is known as "sublinear growth". Another term is "fractional-power" growth but it sounds odd imo.

The sublinear term originates from linear algerba. It can be used not only for square-root but for any $$n-th$$ root complexity.

In strict terms as sublinear function is a function that satisfies the following properties:

• Positive Homogeneity: $$f(kx) = k^n f(x) \quad n\in\mathbb{R^+_0}$$ and
• Subadditivity: $$f(x+y) \leq f(x) + f(y)$$

Roots satisfy both. The proof of positive homogeneity is trivial. As far as the proof of subadditivity is concerned you can check this post

Other seemingly sublinear functions (such as log) do not satisfy these properties therefore, in a sense you can separate them from sublinears.

• My impression is that the term "sublinear" is also applicable to logarithmic growth; is that correct? I am hoping for a term that clearly distinguishes the growth as separate from logarithmic growth. Commented Jul 21, 2020 at 6:07
• @Kevin I edited my answer, to answer to your comment Commented Jul 21, 2020 at 6:17
• Roots do not satisfy "Positive Homogeneity". Commented Jul 21, 2020 at 8:02
• @BrianO $f(kx) = \sqrt k f(x)$ with degree of homogeneity $= \frac12 > 0$. e.g $\sqrt{kx} = \sqrt k \sqrt x$ Commented Jul 21, 2020 at 8:45
• @BrianO I edited my answer so its clearer. Commented Jul 21, 2020 at 8:46

Well since $$y=\sqrt x \implies y^2=x$$, I would call it inverse quadratic growth, i.e. the inverse of the function has quadratic growth.

• We can also write it as $y = x ^ {1/2}$ and call it "fractional quadratic growth", but that doesn't seem right either. Commented Jul 21, 2020 at 6:13