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Prime factorisation, the Fundamental Theorem of Arithmetic, and proving square roots like root 2 are irrational.
Real Numbers
Step-by-step NCERT Class 10 Exercise 1.2 solutions proving that root 5, 3 + 2 root 5, 1 over root 2, 7 root 5 and 6 + root 2 are irrational, using proof by contradiction and the prime divisor theorem.
Real Numbers
Step-by-step proofs by contradiction that root 2 and root 3 are irrational, the prime-divides-square theorem they rest on, and how to show numbers like 5 minus root 3 and 3 root 2 are irrational.
Real Numbers
Full NCERT Class 10 Exercise 1.1 solutions: prime factorisation of five numbers, HCF and LCM of pairs and triples, LCM from a given HCF, why 6ⁿ never ends in 0, two composite numbers and the Sonia and Ravi track problem.
Real Numbers
Why every composite number breaks into primes in exactly one way, and how to use prime factorisation to find the HCF and LCM, decide whether a power can end in 0, and avoid the three-number HCF-LCM trap.
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