Concept explainers
To state: The statement false by finding a counterexample: The product of two irrational numbers is an irrational number.
The statement is false.
Given information:
The given statement is the product of two irrational numbers is an irrational number.
Explanation:
Consider the definition of irrational numbers:
Irrational numbers include numbers that cannot be expressed in terms of
To multiply two irrational numbers use the formula:
Now consider the statement: The product of two irrational numbers is an irrational number.
Counterexample:
Take two irrational numbers
Product of two irrational numbers
Here, 5 is a rational number.
Therefore, the given statement is false.
Chapter 1 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
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