Surds & Indices
Surds & Indices
Indices (exponents) express repeated multiplication; surds are irrational roots that cannot be simplified to rational numbers. Together they appear in simplification, comparison, and algebraic manipulation questions across competitive exams.
Key Idea
Master the 5 index laws and rationalisation — every surd/indices question is a combination of these.
Core Formulas
Product Rule
a^m × a^n = a^(m+n)
When multiplying same base powers
Division Rule
a^m ÷ a^n = a^(m-n)
When dividing same base powers
Power Rule
(a^m)^n = a^(mn)
When raising a power to another power
Negative Index
a^(-n) = 1/a^n
To convert negative exponents to positive
Fractional Index
a^(p/q) = q√(a^p)
To convert fractional exponents to radicals
Relevant Exams
2–3 direct questions per paper in SSC CGL Tier 1 and Tier 2. Mostly evaluate laws of indices and simplification of surds.