Real Numbers — Formula Sheet
Punjab Board · Class 10 · Mathematics
3 formulas from Real Numbers (Punjab Board Class 10 Mathematics) on one page, grouped by topic. Includes Examples of irrational numbers.
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Formulas and Key Relations
The Fundamental Theorem of Arithmetic
Any composite number x can be written as x = p1 × p2 × ... × pn, where p1 ≤ p2 ≤ ... ≤ pn are primes written in ascending order.
Revisiting Irrational Numbers – Proof by Contradiction
Examples of irrational numbers
√2, √3, √5, √15, π, 0.10110111011110...
Key relations
For any two positive integers a and b, the relationship HCF(a, b) × LCM(a, b) = a × b always holds true.
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