The product of two irrational numbers is

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Study for the Algebra 1 Honors End-of-Course Test. Study with flashcards and multiple-choice questions, each question has hints and explanations. Get ready for your exam!

Multiple Choice

The product of two irrational numbers is

Explanation:
The key idea is that multiplying two irrational numbers does not always produce an irrational result. It depends on the numbers involved. For example, multiplying sqrt(2) by sqrt(2) gives 2, which is rational. But multiplying sqrt(2) by sqrt(3) gives sqrt(6), which is irrational. Since neither factor is zero, their product is defined, and you can get either a rational or an irrational number depending on the pair. So the statement isn’t universally true; the product can be rational in some cases and irrational in others.

The key idea is that multiplying two irrational numbers does not always produce an irrational result. It depends on the numbers involved. For example, multiplying sqrt(2) by sqrt(2) gives 2, which is rational. But multiplying sqrt(2) by sqrt(3) gives sqrt(6), which is irrational. Since neither factor is zero, their product is defined, and you can get either a rational or an irrational number depending on the pair. So the statement isn’t universally true; the product can be rational in some cases and irrational in others.

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