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# how to find the 5th root of -32

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how to find the 5th root of -32

Guest Mar 25, 2017
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#1
+6900
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(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
+91247
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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

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