Irrational Numbers
An irrational number is a real number that cannot be written as p/q, where p and q are integers and q is not zero.
Practice This ConceptMain explanation
Teacher explanation
Irrational numbers have decimal expansions that neither terminate nor repeat. Common examples include √2, √3, √5, and π. A square root of a non-perfect square is irrational.
Example
√2 is irrational because it cannot be written exactly as a fraction of two integers, and its decimal form continues without repeating.
Simple analogy
Perfect square root is rational; non-perfect square root stays irrational.
Common confusion
Students sometimes say every square root is irrational, but √4 = 2 and √9 = 3 are rational numbers.
Exam tip
Check whether the number under the square root is a perfect square before deciding whether the square root is rational or irrational.
Study the irrational numbers diagram carefully
Use the labelled diagram to keep irrational numbers clear in short answers and revision.
What this diagram makes clear
This diagram keeps the labels and direction of irrational numbers in the right order.
Where this helps in exams
Use this for labelled diagram work and short exam answers on irrational numbers.
Revision cue
Revise irrational numbers through the labels before writing the answer.
Answer writing and exam use
1-mark use
Write the exact meaning of irrational numbers in one clean line.
2-mark use
Define irrational numbers and add one example or condition.
3-mark use
Explain irrational numbers, show the method or example, and mention the common mistake.
Practice this concept with focused MCQs
Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.
Help improve this page
Found something confusing, incorrect, or missing?