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.

  • $\begingroup$ Please do not put [Answered] in the question name $\endgroup$ – Ariana Jul 7 '16 at 15:12
  • $\begingroup$ @ArianaGrande - why not? $\endgroup$ – Carlos Carlsen Jul 7 '16 at 15:12
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    $\begingroup$ Because this isn't a forum, accepting a answer is enough to demonstrate that it is answered. :-) $\endgroup$ – Zain Patel Jul 7 '16 at 15:13
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    $\begingroup$ @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....:-) $\endgroup$ – tatan Jul 7 '16 at 15:17
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    $\begingroup$ @CarlosCarlsen Ha...ha!! $\endgroup$ – tatan Jul 7 '16 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 $x^4$.

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    $\begingroup$ 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. :) $\endgroup$ – symplectomorphic Jul 7 '16 at 15:24
  • $\begingroup$ Good point! Edited it in. :-) $\endgroup$ – Zain Patel Jul 7 '16 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.

  • $\begingroup$ okay, so square and cubed root are just fancy names? $\endgroup$ – Carlos Carlsen Jul 7 '16 at 15:10
  • $\begingroup$ 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. $\endgroup$ – Arthur Jul 7 '16 at 15:11
  • $\begingroup$ Ah, okay - well thanks a ton!! $\endgroup$ – Carlos Carlsen Jul 7 '16 at 15:11
  • $\begingroup$ @Carlos Carlsen: as I commented above, "cubed root" is not right (we don't say "squared root"); it's "square root" and "cube root." $\endgroup$ – symplectomorphic Jul 7 '16 at 15:18
  • $\begingroup$ I will edit that @symplectomorphic - thanks for the clarification. $\endgroup$ – Carlos Carlsen Jul 7 '16 at 15:19

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