Irrational numbers
An irrational number cannot be written in the form p/q, where p and q are integers and q != 0.
Practice This ConceptMain explanation
Teacher explanation
These numbers have decimal expansions that never end and never repeat. In Class 10, square roots like sqrt(2), sqrt(3), and sqrt(5) become important examples. They are not fractions, even if they look neat on the number line.
Example
sqrt(2) and pi are irrational numbers.
Simple analogy
Rational repeats or ends; irrational does neither.
Common confusion
Students call every non-terminating decimal irrational and forget that repeating decimals are rational.
Exam tip
Check both conditions: the decimal should not end and should not repeat.
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.
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