📘 VEDIC MATH: SQUARE & CUBE TRICKS (Full Guide for Competitive Exams)

📘 VEDIC MATH SQUARE & CUBE TRICKS (Full Guide for Competitive Exams)
📘 VEDIC MATH: SQUARE & CUBE TRICKS (Full Guide for Competitive Exams)
👨🏫 By Grandmaster Bikram Sutradhar
🏆 5× World Record Holder | Best Teacher Awardee | JAM AIR 392
🌐 Visit: sirbikramsutradhar.com
📞 Contact: 9863002294
🧮 PART 1: SQUARE TRICKS (within seconds!)
✅ 1. Square of numbers ending with 5
💡 Use Sutra: Ekadhikena Purvena (One more than the previous)
➡️ Formula: If a number = x5, then (x5)² = x × (x+1) and add 25
🧠 Examples:
- 25² = 2×3 = 6 → Add 25 → 625
- 75² = 7×8 = 56 → Add 25 → 5625
- 95² = 9×10 = 90 → Add 25 → 9025
🟢 Superfast trick for banking/SSC!
✅ 2. Square of numbers near base (100, 1000)
💡 Use Sutra: Nikhilam Navatashcaramam Dashatah (All from 9 and the last from 10)
➡️ For numbers near 100:
Step:
- Find difference from 100 (positive or negative)
- Subtract crosswise
- Multiply difference part
🧠 Example:
97² →
97 is 3 less than 100 → (97 – 3 = 94)
3² = 09
✔️ Answer: 9409
102² →
102 is 2 more → 102 + 2 = 104 → 2² = 04
✔️ Answer: 10404
✅ 3. Square of any 2-digit number (General Trick)
💡 Use: (a + b)² = a² + 2ab + b²
➡️ Split number into tens and unit digits
🧠 Example: 47²
a = 40, b = 7
= 40² + 2×40×7 + 7²
= 1600 + 560 + 49 = 2209
✅ 4. Special Trick: Square of numbers between 50 to 60
Formula:
(50 + x)² = 2500 + 100x + x²
🧠 Example: 53²
= 2500 + 100×3 + 9 = 2809
✅ 5. Square of any number ending in 1, 9, 2, 8
Use formula:
(x + y)² = x² + 2xy + y²
🧠 Example: 39² = (40 – 1)² = 40² – 80 + 1 = 1521
🧮 PART 2: CUBE TRICKS (Fast and Easy)
✅ 1. Cube of numbers ending in 1 to 9 (memorize)
📌 1³ = 1
📌 2³ = 8
📌 3³ = 27
📌 4³ = 64
📌 5³ = 125
📌 6³ = 216
📌 7³ = 343
📌 8³ = 512
📌 9³ = 729
📌 10³ = 1000
🔁 Know these well — very useful in reasoning and simplification.

✅ 2. Cube of 2-digit numbers (Algebra trick)
💡 Formula: (a + b)³ = a³ + 3a²b + 3ab² + b³
🧠 Example: 12³
Split: 10 + 2
= 1000 + 3×100×2 + 3×10×4 + 8
= 1728
✅ 3. Cube of numbers near 100
Use (x ± y)³ = x³ ± 3x²y + 3xy² ± y³
🧠 Example: 101³
= (100 + 1)³ =
1000000 + 3×10000×1 + 3×100×1 + 1
= 1030301
✅ 4. Last digit trick for cubes in options
✅ Cube of number ending with:
Unit Digit | Last Digit of Cube |
1 | 1 |
2 | 8 |
3 | 7 |
4 | 4 |
5 | 5 |
6 | 6 |
7 | 3 |
8 | 2 |
9 | 9 |
0 | 0 |
Helps in eliminating wrong options in MCQs.
✅ 5. Trick for cube of numbers like 11, 21, 31, 41…
11³ = 1331
21³ = 9261
31³ = 29791
➡️ Use (x + 1)³ formula or remember 1st few values.
🧠 Final Tips to Master Vedic Square & Cube Tricks:
✔️ Practice daily for speed
✔️ Don’t memorize blindly — understand the patterns
✔️ Use base method for close-to-100 numbers
✔️ For mental math, always break numbers logically
✔️ Compete with a timer (simulate exam feel)
📘 FREE PRACTICE QUESTIONS (with Answers)
- 95² = ?
- 104² = ?
- 47² = ?
- 62² = ?
- 12³ = ?
- 23³ = ?
- 1001² = ?
- 999² = ?
- Find cube of 41
- 89² = ?
📩 Want answers & PDF?
👉 Comment “SquareCube PDF” or WhatsApp 9863002294
📲 Follow Grandmaster Bikram Sutradhar for more powerful tricks
🌐 sirbikramsutradhar.com
📞 9863002294
🎯 Join Vedic Math Masterclass Now!
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Written By
Full Stack Developer and 5-Time World Record Holder, Grandmaster Bikram Sutradhar
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Written By
Full Stack Developer and 5-Time World Record Holder, Grandmaster Bikram Sutradhar
bAstronautWay
SirBikramSutradhar on YouTube
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ICSE CLASS 10 ICSE CLASS 10 BIOLOGY BASTRONAUTWAY SirBikramSutradhar Bikram Sutradhar GrandMaster Bikram Sutradhar selina biology solutions ICSE Biology Selina Solution
📚 Class 9 Science – Complete Table of Contents (विषय-सूची)
CBSE | NCERT Curriculum | Bilingual (English + Hindi)
By Grandmaster Bikram Sutradhar | SirBikramSutradhar | BASTRONAUTWAY
🔬 PHYSICS (भौतिक विज्ञान)
🔢 | Chapter Title (English) | अध्याय का नाम (हिंदी) | Page No. |
1️⃣ | Motion | गति | |
2️⃣ | Force and Laws of Motion | बल तथा गति के नियम | |
3️⃣ | Gravitation | गुरुत्वाकर्षण | |
4️⃣ | Work and Energy | कार्य तथा ऊर्जा | |
5️⃣ | Sound | ध्वनि |
🧪 CHEMISTRY (रसायन विज्ञान)
🔢 | Chapter Title (English) | अध्याय का नाम (हिंदी) | Page No. |
1️⃣ | Matter in Our Surroundings | हमारे आस-पास के पदार्थ | |
2️⃣ | Is Matter Around Us Pure? | क्या हमारे आस-पास के पदार्थ शुद्ध हैं? | |
3️⃣ | Atoms and Molecules | परमाणु एवं अणु | |
4️⃣ | Structure of the Atom | परमाणु की संरचना |
🧬 BIOLOGY (जीव विज्ञान)
🔢 | Chapter Title (English) | अध्याय का नाम (हिंदी) | Page No. |
1️⃣ | The Fundamental Unit of Life | जीवन की मौलिक इकाई | |
2️⃣ | Tissues | ऊतक | |
3️⃣ | Improvement in Food Resources | धनों में सुधार |
📘 ADDITIONAL SECTIONS (अतिरिक्त अनुभाग)
📖 Section | Title (English + Hindi) |
🔹 | Glossary / पारिभाषिक शब्दावली |
🔹 | Answer Keys / उत्तरमाला |
🔹 | Summary / सारांश |
🔹 | Important Diagrams / महत्वपूर्ण चित्र |
🔹 | NCERT Exercises / एनसीईआरटी अभ्यास |
🔹 | Sample Papers & MCQs / मॉडल पेपर व वस्तुनिष्ठ प्रश्न |
✅ All content follows the official NCERT Class 9 Science textbook structure. Each chapter will include explanations, bilingual notes, definitions, diagrams, MCQs, FAQs, and practice exercises under the BASTRONAUTWAY learning system.
class 10 Maths ncert solution.
CBSE Class 10 Mathematics (2025) NCERT Syllabus:
CBSE Class 10 Mathematics NCERT Syllabus (2025) – Chapter-Wise List
CBSE Class 10 Mathematics NCERT Syllabus (2025) – Chapter-Wise List
chapter 4. Quadratic Equations
chapter 5. Arithmetic Progressions
chapter 6. Triangles
chapter 7. Coordinate Geometry
chapter 8. Introduction to Trigonometry
chapter 9. Some Applications of Trigonometry
chapter 11. Areas Related to Circles
chapter 12. Surface Areas and Volumes
CBSE Class 10 Science (2025) NCERT Syllabus:
CBSE Class 10 Science NCERT Syllabus (2025) – Chapter-Wise List
CBSE Class 10 Science NCERT Syllabus (2025) – Chapter-Wise List
Chapter 1 Chemical Reactions and Equations
Chapter 2 Acids, Bases and Salts
Chapter 3 Metals and Non-metals
Chapter 4 Carbon and its Compounds
Chapter 5 Life Processes
Chapter 6 Control and Coordination
Chapter 7 How do Organisms Reproduce?
Chapter 8 Heredity
Chapter 9 Light – Reflection and Refraction
Chapter 10 The Human Eye and the Colourful World
Chapter 11 Electricity
Chapter 12 Magnetic Effects of Electric Current
Chapter 13 Our Environment
📖 Chapter 12 – Organic Chemistry (Selina Textbook)
Table of Contents:
- 12A. Organic Compounds
- 12B. Hydrocarbons: Alkanes
- 12C. Hydrocarbons: Alkenes
- 12D. Hydrocarbons: Alkynes
- 12E. Alcohols
- 12F. Carboxylic Acids
- Exercise 12 MISCELLANEOUS
- Glossary
- Model Question Paper –
📌 Exercise 12 MISCELLANEOUS – Focus Areas:
- 🧬 Consolidated practice from the entire Organic Chemistry chapter
- 🧪 Application-based questions covering alkanes, alkenes, alkynes, alcohols, and carboxylic acids
- 🧾 Writing structural formulas and chemical equations
- 💡 Distinguishing reactions, isomer identification, and conversions
- 📘 Full-syllabus revision to boost conceptual clarity and board exam readiness
Each question in this section is designed to:
- ✅ Strengthen cross-topic understanding
- 📝 Prepare students for application-based and reasoning-based questions
- 🧠 Improve problem-solving speed and exam performance
class 5
📚 Class 9 Science – Complete Table of Contents (विषय-सूची)
CBSE | NCERT Curriculum | Bilingual (English + Hindi)
By Grandmaster Bikram Sutradhar | SirBikramSutradhar | BASTRONAUTWAY
🔬 PHYSICS (भौतिक विज्ञान)
🔢 | Chapter Title (English) | अध्याय का नाम (हिंदी) | Page No. |
1️⃣ | Motion | गति | |
2️⃣ | Force and Laws of Motion | बल तथा गति के नियम | |
3️⃣ | Gravitation | गुरुत्वाकर्षण | |
4️⃣ | Work and Energy | कार्य तथा ऊर्जा | |
5️⃣ | Sound | ध्वनि |
🧪 CHEMISTRY (रसायन विज्ञान)
🔢 | Chapter Title (English) | अध्याय का नाम (हिंदी) | Page No. |
1️⃣ | Matter in Our Surroundings | हमारे आस-पास के पदार्थ | |
2️⃣ | Is Matter Around Us Pure? | क्या हमारे आस-पास के पदार्थ शुद्ध हैं? | |
3️⃣ | Atoms and Molecules | परमाणु एवं अणु | |
4️⃣ | Structure of the Atom | परमाणु की संरचना |