SOLUTION: If a and b are irrational numbers, do you agree that a�b, ab, and b/a(with a not equal to 0) are always irrational numbers? Why?

Question 974043: If a and b are irrational numbers, do you agree that a�b, ab, and b/a(with a not equal to 0) are always irrational numbers? Why?
Found 2 solutions by CubeyThePenguin, ikleyn:
Answer by CubeyThePenguin(3113)   (Show Source): You can put this solution on YOUR website!
a and b are irrational, so they cannot be written in the form p/q for integers p and q.

a + b, ab, and b/a are always irrational, because if the parts cannot be written as rational numbers, then the total will not be able to be written as one.
Answer by ikleyn(52845)   (Show Source): You can put this solution on YOUR website!
.

            The answer by @CubeyThePenguin is   TOTALLY   and   ABSOLUTELY     W R O N G (!)

For the sum (a + b), the counter-example is   a = ,   b= .

For the product   ,   the counter-example is   a = b = .

For the ratio   ,   the counter-example is the same   a = b = .

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Hello, @CubeyThePenguin, consider to hire somebody, who will assist you by editing / fixing your solutions after you.

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