Thank you for the opportunity to help you with your question!
The square root of a number has to be the square root of a
perfect square in order for that to be a rational number. All whole
number perfect squares are squares of whole numbers. I can even prove to
you that this isn't a rational number by this method:
1²=1, 2²=4, 3²=9, 4²=16, 5²=25, 6²=36,....
As you see 30 is skipped in the perfect squares. So, √30 is
apparently inbetween 5 and 6, but it is not rational, it's irrational.
Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 29th, 2015
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