A fast, one-glance recap of Class 10 Maths Chapter 1 (Real Numbers) — for the full worked explanations, see the Solutions.
Revision Notes: Real Numbers
- Euclid’s Division Lemma: a = bq + r, where 0 ≤ r < b
- Euclid’s Division Algorithm: repeatedly apply the lemma to find HCF — the last non-zero remainder’s divisor is the HCF
- Fundamental Theorem of Arithmetic: every composite number factorises into primes uniquely (order aside)
- HCF × LCM = product of the two numbers (two numbers only, not three or more)
- Proving irrationality: assume rational (p/q, coprime, q≠0) → show p and q share a common factor → contradiction
- Know by heart: √2, √3, √5, and √p for any prime p are irrational; 6n never ends in 0 (no factor of 5)
Keep Going
Full Solutions · Extra Questions (HOTS) · Formulas Handbook
FAQ
Is this enough on its own?
No — use it as a checklist alongside solving problems, not instead of them.
