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Chapter 5: Problem 11

Give an example of a number that is an irrational number and a real number.

Short Answer

Expert verified
An example of a number that is both an irrational number and a real number is \( \sqrt{2}. \)

Step by step solution

01

Understanding Rational and Irrational Numbers

Rational numbers are numbers that can be expressed as a fraction of two integers. An example of a rational number is \( \frac{2}{3} \) or 0.5. On the other hand, an irrational number cannot be expressed as a fraction of two integers. They cannot be written as a simple fraction because there is not a finite number of numbers when they are written as a decimal. Instead, the decimal goes on forever without repeating.
02

Understanding Real Numbers

A real number is a number that can be found on the number line. This includes both rational numbers (such as 7 and \( \frac{1}{2} \)) and irrational numbers (such as the square root of 2 and pi).
03

Give an example of an Irrational Number

An example of an irrational number is \( \sqrt{2} \). It is a real number that is not rational. The decimal representation of \( \sqrt{2} \) (approximately 1.41421356) neither terminates nor repeats.

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