+0  
 
0
167
2
avatar

how to find the 5th root of -32 

Guest Mar 25, 2017
Sort: 

2+0 Answers

 #1
avatar+6765 
0

(Odd number)-th root of a negative number is also a negative number.

\(\sqrt[5]{-32}\\ =-\sqrt[5]{32}\\ =-2\)

MaxWong  Mar 25, 2017
 #2
avatar+89835 
0

Yes     \(\sqrt{-32}=-2\)

And that I think is the only answer BUT

 

if

\(x^5=-32\\ then\\ x=2cis(\pi+\frac{2\pi n}{5})\qquad n \in Z\\ x=2cis(\frac{5\pi}{5}+\frac{2\pi n}{5})\qquad n \in Z\\ x=2cis(\frac{\pi}{5}),\quad x=2cis(\frac{3\pi}{5}),\quad x=2cis(\frac{5\pi}{5}),\quad x=2cis(\frac{7\pi}{5}),\quad x=2cis(\frac{9\pi}{5})\\ x=2cis(\frac{\pi}{5}),\quad x=2cis(\frac{3\pi}{5}),\quad x=-2,\quad x=2cis(\frac{7\pi}{5}),\quad x=2cis(\frac{9\pi}{5})\\ \)

Melody  Mar 26, 2017

14 Online Users

avatar
avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details