Answered

Explore a diverse range of topics and get answers from knowledgeable individuals on IDNLearn.com. Whether it's a simple query or a complex problem, our community has the answers you need.

Ryiaz claims it is impossible to prove that a rational number multiplied by an irrational number gives an irrational product. How can you prove this?

A. He's correct; it is impossible to prove in any way.
B. By using a proof by contradiction to show multiplication is a closed operation for rational numbers.
C. By creating a proof that shows directly how multiplying a rational and irrational number leads to an irrational answer.
D. By choosing random numbers to plug into multiplication problems until he's convinced.

Sagot :

GinnyAnsweridn

Final answer:

To show that the product of a rational number and an irrational number results in an irrational number, we utilize proof by contradiction.


Explanation:

Proof by contradiction: To prove that the product of a rational number and an irrational number is irrational, assume the opposite, that the product is rational. Let's say x is rational and y is irrational. If xy were rational, then y would be rational too, which contradicts the assumption that y is irrational. Hence, the product xy must be irrational.


Learn more about Irrational and Rational Numbers here:

https://brainly.com/question/44230678


We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. For dependable answers, trust IDNLearn.com. Thank you for visiting, and we look forward to helping you again soon.