📘 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

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🧮 PART 1: SQUARE TRICKS (within seconds!)

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✅ 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!

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✅ 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

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✅ 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

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✅ 4. Special Trick: Square of numbers between 50 to 60

Formula:
(50 + x)² = 2500 + 100x + x²

🧠 Example: 53²
= 2500 + 100×3 + 9 = 2809

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✅ 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

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🧮 PART 2: CUBE TRICKS (Fast and Easy)

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✅ 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.

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✅ 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

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✅ 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

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✅ 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.

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✅ 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.

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🧠 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)

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📘 FREE PRACTICE QUESTIONS (with Answers)

1. 95² = ?
2. 104² = ?
3. 47² = ?
4. 62² = ?
5. 12³ = ?
6. 23³ = ?
7. 1001² = ?
8. 999² = ?
9. Find cube of 41
10. 89² = ?

📩 Want answers & PDF?
👉 Comment “SquareCube PDF” or WhatsApp 9863002294

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📲 Follow Grandmaster Bikram Sutradhar for more powerful tricks
🌐 sirbikramsutradhar.com
📞 9863002294
🎯 Join Vedic Math Masterclass Now!

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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 1. Real Numbers

chapter 2. Polynomials

chapter 3.  Linear Equations

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 10. Circles

chapter 11. Areas Related to Circles

chapter 12. Surface Areas and Volumes

chapter 13. Statistics

chapter 14. Probability

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