Surds & Indices
Surds & Indices
Surds and indices questions boil down to five index laws plus rationalization. SSC CGL Tier 1 and Tier 2 each carry 2\u20133 direct questions that test simplification, comparison of powers, and conversion between radical and exponential form. Nail the laws and you convert every problem into a single-step base-matching exercise.
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)
Combine two powers that share the same base into one term by adding exponents.
Division Rule
a^m ÷ a^n = a^(m-n)
Reduce a fraction of same-base powers into one term by subtracting exponents.
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.