Surds and Indices
Surds and indices are important topics in quantitative aptitude that involve powers, roots, and irrational numbers. These concepts are frequently asked in banking, SSC, CMAT, and placement exams.
Fundamental Principles
Indices (Exponents)
Powers of a number representing repeated multiplication.
Surds
Irrational numbers expressed in root form (e.g., √2, √5).
Rationalization
Process of removing surds from denominator.
Essential Formulation Tips
- Memorize laws of indices.
- Convert roots into fractional powers.
- Simplify before calculating.
- Use rationalization for division problems.
Shortcut Execution Techniques
- a^m × a^n = a^(m+n).
- a^m / a^n = a^(m−n).
- (a^m)^n = a^(mn).
- √a = a^(1/2), ∛a = a^(1/3).
Contextual Inquiries (FAQs)
Q: What is the most important law of indices?
A:
Q: How to simplify surds quickly?
A:
Example Breakdown: Indices Example
Basic concept.Use law: a^m × a^n = a^(m+n).
2^(3+4) = 2^7 = 128.
Final Answer: 128.
Example Breakdown: Surd Simplification
Common exam question.√50 = √(25 × 2).
= 5√2.
Final Answer: 5√2.
Example Breakdown: Rationalization Example
Important concept.Multiply numerator and denominator by √2.
= √2 / 2.
Final Answer: √2/2.
Surds & Indices Practice Questions
Solve important surds and indices questions for banking, SSC, CMAT, and placement exams.
Q1. Simplify 3^2 × 3^3.
Q2. Simplify √72.
Q3. Simplify 1/(√5).