Mathematics Class 10
Real Numbers
Break any number into primes, prove the split is unique, and settle √2, √3, √5.
14 lessons · ~112 min total
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Lessons in this topic
- 0 Start here A roadmap: prime factors, HCF and LCM, and the proofs that √2, √3 and √5 are irrational. · 4 min You are here
- 1 Break a number into primes Keep dividing a number by primes. The dividing stops at 1, and the primes multiply back to the number. · 8 min
- 2 One set of primes, HCF and LCM Every composite number has one set of primes. Read HCF and LCM off two such sets. · 9 min
- 3 Squares have even powers In a perfect square, every prime has an even power. Use it to test squares. · 8 min
- 4 A prime that divides a square If a prime divides n², it divides n. This lemma powers every proof in the chapter. · 9 min
- 5 The proof for √2 and √3 One plan proves √2 irrational. The same plan proves √3. · 9 min
- 6 The proof for √5 Suppose a fraction in lowest terms squares to 5. Six lines end in a contradiction. · 10 min
- 7 What a proof settles A proof covers every fraction. A search covers only the ones it tried. · 9 min
- 8 Write the proof in order A written proof has four links. Each link is fed by the one before it. · 8 min
- 9 A number joined to a root Suppose it is a fraction. Get the root alone. A fraction cannot equal an irrational root. · 9 min
- 10 HCF and LCM of three numbers List every prime in all three. HCF takes the smallest power. LCM takes the greatest. · 9 min
- 11 Checkpoint: roots with a partner, and three numbers Five quick checks on roots joined to numbers, and on HCF and LCM of three. · 6 min
- 12 The big picture Ten ideas, tied back together. · 6 min
- 13 Track quiz Cheat-sheet table plus a reveal quiz — one question per idea. · 8 min
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