Surds & Indices
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Quantitative Aptitude - Surds & Indices
Master radical simplification and exponent rules to simplify expressions swiftly.
1. Surds (Radicals)
- Surd form: \( \sqrt{n} \), \( \sqrt[3]{n} \), etc., when \( n \) is not a perfect power.
- Simplify by prime factorization under the root (e.g., \( \sqrt{72} = \sqrt{36 \cdot 2} = 6\sqrt{2} \)).
- Rationalize denominators to remove radicals.
2. Indices (Exponents)
- Basic rules: \( a^m \times a^n = a^{m+n};\; a^m ÷ a^n = a^{m−n};\; (a^m)^n = a^{mn} \).
- Negative exponent: \( a^{−n} = 1/a^n \).
- Fractional exponent: \( a^{m/n} = \sqrt[n]{a^m} \).
3. Combined Expressions
- Combine like bases using exponent laws.
- Convert surd form into exponent form to simplify.
4. Quick Tips
- Always simplify radical part under the root first.
- Cancel exponents immediately when bases match.
- Rationalize by multiplying top and bottom by conjugate if needed.
5. Common Mistakes
- Incorrect exponent rules application.
- Forgetting to rationalize denominators in final form.
6. Revision Checklist
- Practice surd simplification and exponent laws weekly.
- Memorize prime factor pairs for root extraction.
Summary: Simplify surds by extracting squares, apply exponent rules cleanly, rationalize denominators, and use exponent-surd conversions for fast and precise solutions.
Topics
- Number System
- H.C.F. & L.C.M.
- Decimal Fractions
- Simplification
- Square Roots & Cube Roots
- Average
- Problems on Numbers
- Problems on Ages
- Surds & Indices
- Percentage
- Operations on Numbers
- Profit & Loss
- Ratio & Proportion
- Partnership
- Chain Rule
- Time & Work
- Pipes & Cistern
- Time & Distance
- Problems on Trains
- Boats & Streams
- Alligation or Mixture
- Simple Interest
- Compound Interest
- Logarithms
- Area
- Volume & Surface Areas
- Mensuration
- Races & Games of Skill
- Calendar
- Clocks
- Stocks & Shares
- Permutations & Combinations
- Probability
- True Discount
- Banker’s Discount
- Heights & Distances
- Odd Man Out & Series
- Algebra
- Divisibility Rules & Remainder Theorem
- Factorials & Power Cycles
- Progressions (A.P., G.P., H.P.)
- Work & Wages
- Set Theory / Venn Diagrams
- Geometry (Lines, Angles, Triangles, Polygons)
- Coordinate Geometry
- Data Interpretation
- Trigonometry
- Statistics (Mean, Median, Mode)
- Arithmetic Operations
- Quadratic Equations