Q1
Which is irrational?
A√2
B1/2
C0.5
D3
CBSEClass 9 (CBSE)MathematicsCh 1 · Topic 1
Rational and Irrational Numbers
Learning to classify numbers as rational or irrational on the number line.
Core concept
√2 = 1.41421356... continues forever without any repeating pattern, proving it is irrational — this was actually proven by the ancient Greeks using a method called proof by contradiction. √2 can be geometrically constructed and precisely located on the number line using the Pythagoras theorem, by constructing a right triangle with legs of length 1 and drawing an arc with the hypotenuse (√2) onto the number line, demonstrating that irrational numbers, despite their complex decimal form, occupy exact, well-defined positions on the real number line.
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• Rational numbers: expressible as p/q, terminating or repeating decimals.
• Irrational numbers: non-terminating, non-repeating decimals (e.g., √2, π).
• Rational + irrational numbers together form the complete set of real numbers.
• √2 can be geometrically constructed and placed exactly on the number line using the Pythagoras theorem.