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?

Algebra ->  Real-numbers -> 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?      Log On


   

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) About Me  (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(52835) About Me  (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 = 1+%2B+sqrt%282%29,   b= 1+-+sqrt%282%29.


For the product   a%2Ab,   the counter-example is   a = b = sqrt%282%29.


For the ratio   a%2Fb,   the counter-example is the same   a = b = sqrt%282%29.


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