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Chapter 0: Problem 12

Give an example of two irrational numbers whose product is an irrational number.

Short Answer

Expert verified
An example of two irrational numbers whose product is an irrational number is the square root of 3 and pi: \( \sqrt{3} \times \pi \)

Step by step solution

01

Find two irrational numbers

First, let's find two irrational numbers. There are many famous irrational numbers such as the square root of 2, pi, and Euler's number e. We'll choose the square root of 3 and pi as our irrational numbers.
02

Multiply the chosen irrational numbers

Now, let's multiply the two irrational numbers we chose: \( product = \sqrt{3} \times \pi\)
03

Determine if the product is irrational

Since the square root of 3 and pi are not integers, and there is no integer multiple that results in either the square root of 3 or pi, their product is also considered an irrational number. Therefore, an example of two irrational numbers whose product is an irrational number are the square root of 3 and pi: \( \sqrt{3} \times \pi \)

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Most popular questions from this chapter

The first letters of the phrase "Please excuse my dear Aunt Sally" are used by some people to remember the order of operations: parentheses, exponentiation (which we will discuss in a later chapter), multiplication, division, addition, subtraction. Make up a catchy phrase that serves the same purpose but with exponentiation excluded.

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