My Math Forum proof of square root results real numbers

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 September 16th, 2008, 10:29 AM #1 Newbie   Joined: Sep 2008 Posts: 1 Thanks: 0 proof of square root results real numbers Hi I wonder if there a proof for a claim that for any real x, square root of x is also real number Hope you can figure out it for me
 September 16th, 2008, 10:52 AM #2 Senior Member   Joined: May 2008 From: York, UK Posts: 1,300 Thanks: 0 Re: proof of square root results real numbers The claim is untrue, since negative reals have imaginary square roots. However, it is true that the square root of a non-negative real number is a real number, and also that every non-negative real has a non-negative square root. Perhaps one of these statements is what you want?
 September 17th, 2008, 07:40 AM #3 Global Moderator   Joined: Dec 2006 Posts: 20,810 Thanks: 2151 Or perhaps "for any real x, $\sqrt[\tiny{3}]{x}$ is also a real number" was intended.

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