Wednesday, 16 March 2016

irrational numbers - How can (sqrtn)2 for n not a perfect square be an integer?

For any positive integer n, n2=n. This looks pretty obvious, but if the nature of an irrational number is considered it doesn't look that obvious.




I mean, n where n is not a perfect square will be irrational and have an infinite decimal expansion. But consider
17=17.00000000
No number from 0 to 9 will give 0 as the result. That looks like it makes impossible an irrational number squaring to a positive integer, as the only way to get a 0 in all decimal places would be to have all digits on the supposed irrational number 0.



I'm not a maths person, so I may have committed lots of errors, but it doesn't look like there's any big one, understanding it in the level that a non-maths person should have. What's the failure in my reasoning?

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