Irrational numbers
Irrational Numbers is a Grade 8 math concept in Saxon Math Course 3, Chapter 2, where students learn that irrational numbers cannot be expressed as a ratio of two integers and have decimal expansions that are non-terminating and non-repeating. Common examples include pi and the square roots of non-perfect squares, and students learn to locate them on the real number line.
Key Concepts
Property An irrational number is a number that cannot be expressed as a fraction. The square root of any counting number that is not a perfect square is an irrational number.
Examples Which number is irrational? A: $\sqrt{25}=5$, B: $\sqrt{36}=6$, C: $\sqrt{42}$, D: $\sqrt{49}=7$. The answer is C, as 42 is not a perfect square. The number $\pi \approx 3.14159...$ is a famous irrational number because its digits go on forever with no repeating pattern. The side length of a square with an area of $3 \text{ cm}^2$ is $\sqrt{3}$ cm, which is an irrational number.
Explanation Think of irrational numbers as the wild ones of the number world! Unlike their rational cousins, their decimal forms go on forever without ever repeating a pattern. You can't pin them down as a simple fraction, which is why your calculator screen fills up with digits when you try to find the value of $\sqrt{2}$!
Common Questions
What is an irrational number?
An irrational number is a real number that cannot be written as a fraction of two integers. Its decimal form is non-terminating and non-repeating, with no pattern that ever ends or repeats.
What are common examples of irrational numbers?
Common examples include pi (approximately 3.14159...), the square root of 2, the square root of 3, and the square root of any non-perfect square.
How do you identify if a square root is irrational?
If the number under the square root sign is not a perfect square, the square root is irrational. For example, the square root of 7 is irrational because 7 is not a perfect square.
Where do irrational numbers fit in the real number system?
Irrational numbers are part of the real number system alongside rational numbers. Together, rationals and irrationals make up all real numbers.
Where are irrational numbers taught in Grade 8?
Irrational numbers are covered in Saxon Math Course 3, Chapter 2: Number and Operations and Geometry.