Irrational numbers
Number systems · Mathematics
Study notes
Q: Prove √3 is irrational (by contradiction). Step 1: Assume √3 = p/q in lowest terms (no common factor). Step 2: Square: 3 = p²/q² → p² = 3q². So 3 divides p², hence 3 divides p. Write p = 3k. Step 3: Then 9k² = 3q² → q² = 3k². So 3 divides q too. Step 4: Both p and q divisible by 3 — contradicts 'lowest terms'. So √3 is irrational.