In Banking exams (IBPS PO, SBI Clerk, RRB PO, SSC CGL), you cannot afford to waste time calculating
squares like 48 × 48 on paper. Every extra second you take on one question is a second
stolen from another. The students who clear the Quantitative Aptitude cutoff with flying colors aren't
necessarily smarter — they've simply mastered calculation shortcuts that let them solve in 10 seconds
what others solve in 60.
This comprehensive guide covers everything you need to know about Squares and Square Roots for competitive exams — from basic tricks to advanced methods used by IBPS PO toppers. Read it once, practice the examples, and your calculation speed will never be the same.
Why Squares & Square Roots Are Critical for Competitive Exams
Before diving into the tricks, let's understand the exam context:
- Simplification: Nearly every BODMAS-based question involves squaring some value
- Number Series: Square-based series (1, 4, 9, 16, 25...) appear in every IBPS exam
- Data Interpretation: DI questions from SBI PO routinely require square root approximations
- Approximation: Rounding to nearest perfect square is the fastest estimation strategy
- Quadratic Equations: Discriminant (b²-4ac) always involves a square calculation
From 2021-2024 IBPS PO Pre analysis: an average of 11 out of 35 questions in the Quantitative section directly or indirectly required knowledge of squares/roots. That's 31% of the section!
Trick 1: Numbers Ending with 5 (Fastest Method)
This is the #1 trick every banking aspirant must master first. Any number ending in 5 can be squared in under 3 seconds.
Formula: (n5)² = [n × (n+1)] followed by 25
Trick 2: Base 50 Method (For Numbers Near 50)
The "Golden Number" here is 25. This works for any number within ±15 of 50, which covers a huge range (35 to 65) commonly seen in exam questions.
Formula: n² = (25 ± deviation) | (deviation²) where deviation = n - 50
Trick 3: a² - b² Method (Difference of Squares)
This is incredibly useful for mental arithmetic in DI and Simplification. The formula is: a² - b² = (a+b)(a-b)
This trick appears when exam questions ask: "Find the value of 63² - 57²" or "Simplify: 99² - 1²"
Trick 4: Square Root — The End Digit Method
Every perfect square has a predictable last digit. Memorize this table once and you'll never struggle with "which option is the square root?" type questions.
| If number ends in | Square root ends in | Exam Application |
|---|---|---|
| 1 | 1 or 9 | Two possibilities — use the "nearest cube" method to choose |
| 4 | 2 or 8 | Two possibilities |
| 5 | 5 | Only one possibility — instant! |
| 6 | 4 or 6 | Two possibilities |
| 9 | 3 or 7 | Two possibilities |
| 0 | 0 | Only one possibility |
Trick 5: Square of Numbers Near 100 (Base Method)
We saw the Base 50 method — here's the Base 100 version, perfect for squares in the 90-110 range.
Formula: n² = (100 ± deviation) | (deviation²) where deviation = n - 100
Trick 6: Approximation for Non-Perfect Squares
For Approximation questions where exact square roots aren't needed, use this formula: √(n²+r) ≈ n + r/(2n)
Exam Strategy: When to Use Which Trick
Having the tricks is not enough — knowing which to apply in each situation is the real skill of a topper:
- Number ends in 5? → Use Trick 1 (n×(n+1) | 25). No other method needed.
- Number between 35-65? → Use Trick 2 (Base 50 method).
- Number between 85-115? → Use Trick 5 (Base 100 method).
- Finding square root of a perfect square? → Use Trick 4 (End Digit method).
- Approximation needed for non-perfect square? → Use Trick 6 (Formula method).
- Simplifying a² - b²? → Instantly apply Trick 3 without calculation.
Common Exam Patterns to Watch For
Based on IBPS PO 2020-2024 question analysis, these are the most frequently tested square/root patterns:
- Pattern 1: "√(7056 + 1944 + ?) = 99" — requires knowing 99² = 9801
- Pattern 2: "If x = √(0.0625), then x = ?" — requires root of decimals (√0.0625 = 0.25)
- Pattern 3: "(√169 × √25) / √(6.25) = ?" — multiple roots in one question
- Pattern 4: "Which of the following is a perfect square? (a) 1764 (b) 1765 (c) 1766" — use end digit rule instantly (4 → ends in 2 or 8)
Frequently Asked Questions (FAQ)
Q: Do I need to memorize squares up to 50?
A: Yes, absolutely. Squares from 1² to 30² should be instant recall. From 31² to 50², you can use the
Base 50 method, but eventually memorizing them saves even more time. Start with 1-20, then 21-30, then
tackle 31-50.
Q: What if a number doesn't end in the digits listed in the End Digit table?
A: If a number ends in 2, 3, 7, or 8, it is NEVER a perfect square. This alone
eliminates wrong options in exam MCQs without any calculation.
Q: How long to master these tricks?
A: 2 weeks of daily 15-minute practice is enough to make all 6 tricks automatic. After that, maintenance
through Ikkish Prep's Simplification module keeps the skills sharp.
Practice these tricks daily on Ikkish Prep's Speed Math Quiz and watch your Quantitative Aptitude score transform!