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is the square root of 1,000 rational

 May 14, 2018
 #1
avatar+3731 
+1

Yes, it is rational; 31.662, and it goes on.

smileysmiley

 May 14, 2018
 #2
avatar+971 
+3

\(\sqrt{1000} = \sqrt{100\cdot10} = \sqrt{100}\cdot\sqrt{10} = 10\sqrt{10}.\)

 

It's irrational since √10 is irrational since there exists NO integer which, when squared, = 10.

 May 14, 2018

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