SOLUTION: Hello. I need some help with an irrational number problem. "Are irrational numbers closed under subtraction? How about division? If not, give an example as to why." Any help

Question 155908: Hello. I need some help with an irrational number problem.
"Are irrational numbers closed under subtraction? How about division? If not, give an example as to why."
Any help would be much appreciated. Thanks in advance!
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
No irrational numbers are not closed under subtraction. Take this example . Since , this shows that 0 is rational (not irrational). So this means that subtraction is not closed over the irrationals (since we found a counter-example)

The same answer applies to division. Notice how and . So this shows us that division of irrational numbers can result in a rational number. So this also means that division is not a closed over the irrational numbers

Note: remember, the term "closed" just means that if you apply an operation to two numbers in a given set, then the result will be a number in that same set. For example, addition over the real numbers is closed since adding any two real numbers results in a real number.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Are irrational numbers closed under subtraction?
No: sqrt(2) - sqrt(2) = 0 which is not irrational.
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How about division? If not, give an example as to why.
No: [sqrt(2)/sqrt(2)] = 1 which is not irrational.
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Cheers,
Stan H.
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