Day 3 · Irrational Numbers & HCF/LCM via Prime Factorisation

An irrational number cannot be written as a fraction p/q (q≠0) — its decimal expansion is non-terminating and non-repeating! For example, √2, √3, π.

In contrast, a rational number's decimal expansion either terminates (like 0.5) or repeats (like 0.333...).

HCF of 6 and 20: 6 = 2×3, 20 = 2²×5 — the only common factor is 2 (smallest power), so HCF = 2.

Activity: Try telling which of 0.75 and √5 is rational and which is irrational.