SMO Senior · 1. Algebraic expressions, radicals, exponents and logarithms
Spot the structure first: identities, conjugates, a common base. Then a long calculation becomes a few exact lines.
Use the square, cube and reciprocal-pair identities to evaluate expressions without long arithmetic.
Simplify radicals with conjugates and nested roots, and find integer parts exactly.
Compare powers and transform logarithms with the power, product and change-of-base rules, respecting domains.
Factorise expressions in several letters by substitution and write a complete Round 2 proof.