How do you say: $\sqrt[z] x$ where $z > 3$?

Question

My whole mathematics is in chaos right now.... I forgot how to say: $\sqrt[z] x$ and I don't know where else to ask -

I know how to say ${d}\sqrt x$ - this is just: $d$ times the square root of $x$;
Also, ${d}\sqrt[3] x$: $d$ times the cube root of $x$;

But, what if $z > 3$?

Would you say, $d$ times the fourth root [or fifth, sixth, etc. depending on your variable $z$] of $x$?

Thanks for your help - I know this is probably simple, but I really don't know what it would be called in order for me to Google it.

Answer 1

We say "the $z$-th root of $x$". You could also say "$x$ to the power $1/z$" which has the benefit of working for non-naturals.

On a side note, for what it's worth, I would read d$\sqrt{x}$ as "$d$ square root of $x$", I wouldn't use the "times".

As you've remarked, square and cube root are just fancy names, just as they are for the indices; we say $x^2$ and $x^3$ as $x$ squared and $x$ cubed, but $x^4$ as $x$ to the power of four.

As pointed out by symplectomorphic: most people say $x$ to the fourth for $x^4$.

Answer 2

Yes. We call them fourth root, fifth root, and so on. It gets hairy for non-natural numbers, but in that case you're better off using exponents anyways.