answersLogoWhite

0

The product is still irrational. Proof by contradiction:

Let X and Y be an element of Q (the set of rational numbers). Thus xy can be written in the form p/q, where p, q are an element of Z (the set of integers), and q is NOT zero. Since X is rational (given in question), it can be written as r/s. Again, r,s are elements of Z and s is not equal to zero.

This gives Y=ps/qr, which is also an element of Q (rationals). However, we know that Y is not rational (given in the question), hence this is the contradiction. Hence the product of a rational and an irrational is irrational.

User Avatar

Wiki User

14y ago

Still curious? Ask our experts.

Chat with our AI personalities

ProfessorProfessor
I will give you the most educated answer.
Chat with Professor
RossRoss
Every question is just a happy little opportunity.
Chat with Ross
MaxineMaxine
I respect you enough to keep it real.
Chat with Maxine
More answers

as0*root2=0 .i.e rational

User Avatar

Wiki User

14y ago
User Avatar

Add your answer:

Earn +20 pts
Q: Product of irrational and rational
Write your answer...
Submit
Still have questions?
magnify glass
imp