Square Root and Cube Root
Square root and cube root are important topics in quantitative aptitude involving powers and roots. These are widely used in simplification, number system, and approximation problems.
Fundamental Principles
Square Root
A number which when multiplied by itself gives the original number (√a).
Cube Root
A number which when multiplied three times gives the original number (∛a).
Perfect Square
A number whose square root is an integer (e.g., 25, 36).
Perfect Cube
A number whose cube root is an integer (e.g., 27, 64).
Essential Formulation Tips
- Memorize squares up to 30 and cubes up to 20.
- Break numbers into prime factors.
- Use approximation for non-perfect squares.
- Practice mental calculation techniques.
Shortcut Execution Techniques
- √(a×b) = √a × √b.
- ∛(a×b) = ∛a × ∛b.
- Last digit trick for cube roots (e.g., cube of 3 ends in 7).
- Group digits in pairs (square root) or triples (cube root).
Contextual Inquiries (FAQs)
Q: How to find square root quickly?
A:
Q: What is the easiest way to find cube roots?
A:
Example Breakdown: Perfect Square Example
Basic concept.144 = 12 × 12.
√144 = 12.
Final Answer: 12.
Example Breakdown: Perfect Cube Example
Common exam question.216 = 6 × 6 × 6.
∛216 = 6.
Final Answer: 6.
Example Breakdown: Simplification Example
Shortcut-based question.√(36 × 25) = √36 × √25.
= 6 × 5 = 30.
Final Answer: 30.
Square & Cube Root Practice Questions
Solve important root-based questions for banking, SSC, CMAT, and placement exams.
Q1. Find √169.
Q2. Find ∛125.
Q3. Find √(49 × 16).