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

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.

• Please do not put [Answered] in the question name Jul 7, 2016 at 15:12
• @ArianaGrande - why not? Jul 7, 2016 at 15:12
• Because this isn't a forum, accepting a answer is enough to demonstrate that it is answered. :-) Jul 7, 2016 at 15:13
• @CarlosCarlsen Even of you don't write the word [ANSWERED] in the title people will anyway come to know it has been answered because in the homepage of the site where the question is displayed...there is a box which shows how many answers a question has got....:-) Jul 7, 2016 at 15:17
• @CarlosCarlsen Ha...ha!! Jul 7, 2016 at 15:19

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 $x^4$.

• I don't know anyone who says "x to the power of four" -- what a tedious mouthful. Rather, we say "x to the fourth," adding "power" at the end if absolutely necessary. :) Jul 7, 2016 at 15:24
• Good point! Edited it in. :-) Jul 7, 2016 at 15:25

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.

• okay, so square and cubed root are just fancy names? Jul 7, 2016 at 15:10
• Yes, because they are so common, and so closely connected to the classical geometric objects square and cube. There is nothing wrong with saying "third root", but "second root" is unusual. Jul 7, 2016 at 15:11
• Ah, okay - well thanks a ton!! Jul 7, 2016 at 15:11
• @Carlos Carlsen: as I commented above, "cubed root" is not right (we don't say "squared root"); it's "square root" and "cube root." Jul 7, 2016 at 15:18
• I will edit that @symplectomorphic - thanks for the clarification. Jul 7, 2016 at 15:19