I was working on math and I had to solve this problem:

Rewrite the expression in radical form: $z^\frac{3}{4}$

My first attempt was wrong: $4 \sqrt {z^3}$
I was confused as to why this was wrong until I saw the difference between the two solutions. This got me thinking: why are they different? (and in fact, I don't know how to say: $\sqrt [4]{z^3}$)
If you wouldn't mind, because I don't know what it's called, could you please explain the differences between the two solutions? (and maybe how to say the former ;) )

Thanks for you time!

  • $\begingroup$ is $z$ a complex number? $\endgroup$ – Dr. Sonnhard Graubner Dec 21 '16 at 15:40
  • $\begingroup$ First one is the forth root of $z^3$ and the second one is four times the square root of $z^3$. $\endgroup$ – MrYouMath Dec 21 '16 at 15:42
  • $\begingroup$ @Dr.SonnhardGraubner no, $z$ is not a complex number. $\endgroup$ – Carlos Carlsen Dec 21 '16 at 15:43

$\sqrt [4]{z^3}=z^{3/4}$ and $4 \sqrt {z^3}=4 \times z^{3/2}.$ i.e. the former is the fourth root of $z^3$ and the latter is multiplying the square root of $z^3$ by $4.$

  • $\begingroup$ Awesome, thanks for the information! $\endgroup$ – Carlos Carlsen Dec 21 '16 at 15:48

it is $$4\sqrt{z^3}=4z^{3/2}$$ and $$\sqrt[4]{z^3}=z^{3/4}$$


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.