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As I know of proportionality, if two things are proportional in degree one, changing (increasing or decreasing) one of them by a factor of say $z$ changes the other by same factor $z$ but what I don't understand is what if the relation is in degree two or higher? Like this question I'm given.

In projectile motion, $H ∝ u²$. If you wish to triple the height($H$), what velocity ($u$) should you give the particle?

What I was thinking was, that: $$√H ∝ u$$ This doesn't let me move forward. If I make that $√H$, $3H$, by multiplying with $√3H$, the other side would get an $H$. I don't know even if I'm thinking it right. I wish someone could help.

Also I couldn't find suitable tags.

Rew
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you would take the square root of the factor you want to increase height by in this case: $$\sqrt{3}\approx 1.73205080757\ldots$$

At least it wasn't Mersenne's laws of strings:

$$f\propto {1\over2L}\sqrt{F\over w}$$

which means, for a constant length of string, you need to either quadruple the tension, or quarter the weight per unit length, to get double the frequency (or some mix).