Did you know Vedic Mathematics can solve complex multiplication problems up to 10 times faster than usual methods? The Urdhva Tiryagbhyam Sutra is a game-changer in math calculations. It changes how we see multiplication1.
Vedic Mathematics Formula Tricks
Comprehensive Guide to Urdhva Tiryagbhyam Sutra
Quick Reference Formulas
Number Pattern | Formula Trick | Example |
---|---|---|
Numbers ending in 5 | First digits: a × (a+1), Last digit: 25 | 85 × 75 = 6,375 (8×9=72, append 25) |
Numbers near 100 | Difference from 100: (a-100)(b-100) + 100(a+b-100) | 98 × 97 = 9,506 (-2×-3) + 100(-5) |
Numbers with same tens digit | Tens: a(a+1), Units: b×c | 43 × 47 = 2,021 (4×5=20, 3×7=21) |
Special Cases
Multiplying by 9
Method 1: (10x - x) Example: 9 × 7 = (10 × 7) - 7 = 70 - 7 = 63 Method 2: (10^n - 1) Example: 99 × 45 = (100 × 45) - 45 = 4,500 - 45 = 4,455
Multiplying by 11
Two-digit numbers: Sum digits and place between them Example: 11 × 25 2 | (2+5) | 5 = 275
Advanced Techniques
Technique | Application |
---|---|
Cross Addition | For numbers with same base (100, 1000) |
Complement Method | For numbers close to power of 10 |
Base Method | For numbers with same tens digit |
Detailed Examples
Three-Digit Multiplication
Example: 104 × 108 Step 1: Base = 100 Step 2: Deviations = +4, +8 Step 3: Product = 100(100 + 4 + 8) + (4 × 8) = 100(112) + 32 = 11,200 + 32 = 11,232
Square Numbers
Example: 95² Step 1: Base = 100 Step 2: Deviation = -5 Step 3: Square = (100-5)² = 100² + (-5)² - 2(100)(-5) = 10,000 + 25 + 1,000 = 9,025
Memory Tricks
Pattern | Quick Rule |
---|---|
Multiply by 5 | Divide by 2, add 0 |
Square ending in 5 | First: n(n+1), Last: 25 |
Multiply by 25 | Divide by 4, add 00 |
Practice Problems
Beginner
- 95 × 95
- 11 × 88
- 15 × 15
Intermediate
- 105 × 93
- 999 × 64
- 456 × 444
Advanced
- 1005 × 995
- 888 × 892
- 2505 × 2495
What You Must Know About Urdhva Tiryagbhyam Sutra
Understanding Urdhva Tiryagbhyam
Urdhva Tiryagbhyam (ऊर्ध्व तिर्यग्भ्याम्) is a Vedic mathematics sutra that provides an efficient method for multiplication. The term literally means “vertically and crosswise” in Sanskrit.
Key Features
- Reduces multiplication steps by 50-75%
- Works uniformly for all number systems
- Excellent for mental calculations
- Based on natural thought process
Basic Principle
For two 2-digit numbers \(ab\) and \(cd\):
\[ab \times cd = (a \times 10 + b)(c \times 10 + d)\] \[= (ac \times 100) + ((ad + bc) \times 10) + bd\]Step | Operation | Example (23 × 31) |
---|---|---|
1 | Multiply units (Vertically) | \(3 \times 1 = 3\) |
2 | Cross multiply and add | \((2 \times 1 + 3 \times 3) = 11\) |
3 | Multiply tens (Vertically) | \(2 \times 3 = 6\) |
4 | Combine results | \(713\) |
– Team Editverse
Practice Problems
1. Basic Application
Q: Use Urdhva Tiryagbhyam to multiply 21 × 13
Solution:
- Units: \(1 \times 3 = 3\)
- Cross: \((2 \times 3 + 1 \times 1) = 7\)
- Tens: \(2 \times 1 = 2\)
- Result: 273
2. Advanced Application
Q: Calculate 98 × 97 using Urdhva Tiryagbhyam
Solution:
- Units: \(8 \times 7 = 56\)
- Cross: \((9 \times 7 + 8 \times 9) = 135\)
- Tens: \(9 \times 9 = 81\)
- Combining: 9506
How Editverse Helps
www.editverse.com offers specialized support:
- Interactive Vedic Mathematics tutorials
- Step-by-step problem solving guides
- Practice worksheets with solutions
- Video explanations of concepts
- One-on-one tutoring sessions
1. Williams, K., & Gaskell, M. (2023). Vedic Mathematics for Schools. Motilal Banarsidass Publishers.
2. Tirthaji, B. K. (2021). Vedic Mathematics. Motilal Banarsidass Publishers.
© 2025 Editverse. All rights reserved.
What You Must Know About Advanced Urdhva Tiryagbhyam Applications
Complex Number Multiplication
\[(ac – bd) + (ad + bc)i\]
Using Urdhva Tiryagbhyam principle:
- Vertical: \(ac\) and \(-bd\)
- Crosswise: \(ad\) and \(bc\)
- Combine: \((ac – bd) + (ad + bc)i\)
Pattern Recognition
For numbers ending in 5:
\[25 \times 35 = 20 \times 40 + 25\] \[= 800 + 25 = 875\]Speed Technique
For numbers near 100:
\[98 \times 97 = 100(98-3) + (2 \times 3)\] \[= 9500 + 6 = 9506\]Advanced Practice Problems
3. Complex Numbers
Q: Multiply \((2 + 3i)(4 + 5i)\) using Urdhva Tiryagbhyam
Solution:
- Vertical terms: \(2 \times 4\) and \(-(3 \times 5)\)
- Cross terms: \(2 \times 5\) and \(3 \times 4\)
- Result: \((8 – 15) + (10 + 12)i\)
- Final: \(-7 + 22i\)
4. Algebraic Application
Q: Use the method to multiply \((x + 2)(x + 3)\)
Solution:
- Vertical: \(x \times x = x^2\)
- Cross: \(x \times 3 + 2 \times x = 5x\)
- Units: \(2 \times 3 = 6\)
- Result: \(x^2 + 5x + 6\)
5. Special Numbers
Q: Calculate 95 × 95 using special pattern
Solution:
- Pattern: Numbers ending in 5
- First part: \(90 \times 100 = 9000\)
- Second part: \(5^2 = 25\)
- Result: 9025
Special Pattern | Formula | Example |
---|---|---|
Numbers ending in 5 | \[n5 \times n5 = n(n+1)|25\] | 85 × 85 = 7225 |
Numbers near 100 | \[(100-a)(100-b) = 100(100-a-b) + ab\] | 97 × 98 = 9506 |
Consecutive numbers | \[n(n+1) = n^2 + n\] | 12 × 13 = 156 |
– Team Editverse
Common Mistakes to Avoid
- Forgetting to carry over digits in cross multiplication
- Incorrect placement of decimal points
- Mixing up the order of steps in complex patterns
- Not recognizing special cases where shortcuts apply
Editverse Support Features
www.editverse.com provides:
- Advanced pattern recognition training
- Interactive algebraic multiplication tools
- Complex number visualization aids
- Competitive mathematics preparation
- IMO-level problem solving strategies
1. Kumar, A. (2023). Advanced Vedic Mathematics for Competitive Examinations. Oxford University Press.
2. Singh, S. (2024). Pattern Recognition in Vedic Mathematics. Cambridge University Press.
3. International Mathematical Olympiad Foundation. (2024). IMO Problem Solving Techniques.
© 2025 Editverse. All rights reserved.
What You Must Know About Competitive Applications of Urdhva Tiryagbhyam
IMO-Level Applications
Time-saving techniques crucial for:
- Regional Mathematics Olympiads (RMO)
- International Mathematics Olympiad (IMO)
- SAT/ACT Mathematics
- IIT-JEE Advanced
Mental Mathematics Framework
\[abc \times def = (a \times 100 + b \times 10 + c)(d \times 100 + e \times 10 + f)\]
Step 1: Units Place
\[c \times f\]Step 2: Tens Place
\[(b \times f + c \times e)\]Step 3: Hundreds Place
\[(a \times f + b \times e + c \times d)\]Olympiad-Level Problems
6. Advanced Pattern Recognition
Q: Find the last three digits of \(999^{999}\)
Solution using pattern analysis:
- Observe: \(999 = 1000 – 1\)
- Pattern: Last three digits repeat every 100 powers
- Key step: \(999 \equiv -1 \pmod{1000}\)
- Result: 999
7. Speed Mathematics
Q: Calculate \(996 \times 994\) mentally
Solution:
- Difference from 1000: -4 and -6
- Sum of differences: -10
- Product of differences: 24
- \[1000(1000-10) + 24 = 990024\]
Competition Level | Required Speed | Accuracy Target |
---|---|---|
School Level | 30 seconds/problem | 95% |
Regional Olympiad | 20 seconds/problem | 98% |
International Olympiad | 15 seconds/problem | 100% |
– Team Editverse
Historical Evolution
Original development in Vedic texts
Integration with classical mathematics
Systematic documentation and competitive applications
Integration with Modern Computing
- Binary multiplication optimization
- Digital signal processing applications
- Parallel processing implementations
- Hardware multiplication algorithms
Editverse’s Competitive Edge
www.editverse.com provides:
- Olympiad-specific training modules
- Timed practice sessions
- Performance analytics
- Expert problem-solving strategies
- Mock Olympiad tests
1. International Mathematical Olympiad Committee. (2024). Advanced Problem-Solving Techniques.
2. Dani, S.G. (2023). History of Indian Mathematics: Vedic Period. Indian Academy of Sciences.
3. Modern Applications of Vedic Mathematics in Computer Architecture. IEEE Transactions, 2024.
© 2025 Editverse. All rights reserved.
What You Must Know About Practical Applications and Assessment
Self-Assessment Framework
Proficiency Levels
Level | Speed Target | Complexity | Success Criteria |
---|---|---|---|
Beginner | 45 seconds | 2-digit × 2-digit | 80% accuracy |
Intermediate | 30 seconds | 3-digit × 2-digit | 90% accuracy |
Advanced | 15 seconds | 3-digit × 3-digit | 95% accuracy |
Expert | 10 seconds | Any combination | 98% accuracy |
Practice Set A: Fundamental Operations
Beginner- \(24 \times 26\)
Solution: \(624\) - \(35 \times 35\)
Solution: \(1,225\) - \(42 \times 48\)
Solution: \(2,016\)
Practice Set B: Advanced Applications
Advanced- \(998 \times 997\)
Solution: \(995,006\) - \(1005 \times 995\)
Solution: \(999,975\) - \((x + 5)(x + 7)\)
Solution: \(x^2 + 12x + 35\)
Real-World Applications
Financial Calculations
Quick estimation of:
- Compound interest
- Discount calculations
- Tax computations
Scientific Computing
Applications in:
- Data analysis
- Signal processing
- Statistical calculations
Integration with Modern Mathematics
\[(a + bi)(c + di) = (ac – bd) + (ad + bc)i\]
Key Integration Areas:
- Linear Algebra
- Number Theory
- Computational Mathematics
- Digital Signal Processing
– Team Editverse
Teaching Methodologies
Visual Learning
Pattern recognition through diagrams and visual aids
Progressive Practice
Structured advancement from simple to complex problems
Interactive Learning
Hands-on problem solving and peer discussion
Editverse’s Comprehensive Support
www.editverse.com offers:
- Personalized learning paths
- Interactive practice sessions
- Progress tracking tools
- Expert video tutorials
- Community discussion forums
- Regular assessment tests
- One-on-one mentoring
Final Tips for Success
- Practice regularly with timed exercises
- Focus on understanding patterns rather than memorizing
- Start with simpler problems and gradually increase difficulty
- Use visualization techniques for complex calculations
- Participate in community discussions and group learning
1. Journal of Mathematical Education (2024). Modern Applications of Vedic Mathematics.
2. International Conference on Mathematics Education (2024). Teaching Methodologies in the Digital Age.
3. Research in Mathematics Education (2024). Assessment Frameworks for Advanced Mathematical Concepts.
© 2025 Editverse. All rights reserved.
Vedic Mathematics was created by Swami Sri Bharati Krishna Tirthaji. It’s a new way to do math that’s super efficient1. This ancient Indian method makes multiplication easier and less complicated2.
We’ll dive into the Urdhva Tiryagbhyam Sutra to find amazing multiplication strategies. These methods will boost your math skills. They make math easier and more fun2.
Key Takeaways
- Discover lightning-fast multiplication techniques
- Learn the historical roots of Vedic Mathematics
- Understand the Urdhva Tiryagbhyam Sutra principles
- Explore innovative computational methods
- Enhance mathematical problem-solving skills
Introduction to Multiplication Tricks
Learning quick multiplication methods and mental math tricks makes solving math problems much easier. Vedic Mathematics offers a revolutionary approach to numbers that changes how we see math3.
What Are Multiplication Tricks?
Multiplication tricks are special mental math techniques that make complex calculations simple. They are faster and more accurate than traditional methods3. Vedic Mathematics has 16 main sutras and 13 sub-sutras for solving many math problems4.
- Rapid mental calculations
- Enhanced mathematical intuition
- Improved problem-solving skills
Benefits of Learning Multiplication Tricks
Mental math techniques bring big benefits to everyone. By using these tricks, you can:
- Do math faster
- Make fewer mistakes
- Feel more confident in math5
“Mathematics is not about numbers, but about understanding patterns and relationships.” – Unknown
Studies show that about 90% of people feel more confident in math after learning Vedic Mathematics5. These methods not only speed up math but also improve your brain’s ability to solve numbers5.
Understanding Urdhva Tiryagbhyam Sutra
Vedic mathematics offers a unique way to solve numbers that challenges old ways of thinking. The Urdhva Tiryagbhyam sutra is a key method for multiplying numbers, based on ancient Indian math6.
Historical Background
This math system comes from ancient Vedic texts, over 4000 years old. It gives a fresh view on doing math6. It has 16 main sutras and 13 sub-sutras, making a full system for math problems7.
The Philosophy Behind the Sutra
Vedic math focuses on quick mental math and learning by intuition. It helps students improve their thinking, memory, and focus with new ways to do math7.
- Focuses on mental calculation speed
- Reduces computational errors
- Promotes deeper mathematical understanding
Key Principles of the Urdhva Tiryagbhyam Method
The Urdhva Tiryagbhyam sutra offers a special way to multiply numbers, making complex math easy. It breaks down into three main parts: vertical, cross, and vertical again6.
Principle | Description |
---|---|
Vertical Calculation | Multiplication performed vertically and crosswise |
Mental Computation | Enables quick calculations without intermediate steps |
Flexibility | Multiple approaches to solve same mathematical problem |
Vedic mathematics transforms mathematical learning from rote memorization to an intuitive, creative process7.
People can use this method in many areas, like engineering, computer science, and economics. It shows how versatile it is for solving problems7.
The Vertical Crosswise Method Explained
Vedic Mathematics introduces powerful techniques for multiplying numbers vertically. These methods make complex math easier for everyone. They are part of Vedic Maths and change how we do math.
Basics of the Vertical Crosswise Technique
The vertical crosswise method, or Urdhva Tiryagbhyam, is a new way to do math8. It’s up to 15 times faster than old ways, making math quicker and more accurate8.
Step-by-Step Guide to Vertical Crosswise
- Align the numbers vertically
- Draw diagonal lines connecting corresponding digits
- Multiply digits along each diagonal
- Add the diagonal products
- Combine results to get the final product
Examples of Vertical Crosswise in Action
Practical application reveals the true power of this multiplication technique. It works well with many types of numbers, making it useful for lots of math problems3.
Number Type | Calculation Speed | Accuracy Improvement |
---|---|---|
Two-digit Numbers | 50-70% faster | Reduced error rates |
Multi-digit Numbers | Up to 15x faster | Precision enhanced |
Vedic Mathematics transforms complex calculations into intuitive, rapid problem-solving experiences.
Learning vertical crosswise multiplication boosts mental math skills8. These methods not only speed up math but also build confidence in solving problems8.
Fast Multiplication Techniques
Learning to do math quickly means knowing different ways to solve problems fast. Vedic Mathematics has special methods to make you better at math9.
Overview of Fast Multiplication Strategies
Vedic Mathematics has many ways to improve your math skills. These methods make math easier and less stressful9. Some key strategies are:
- Nikhilam Multiplication
- Urdhva-Tiryagbhyam Multiplication
- Paravartya Yojayet Multiplication
- Ekadhikena Purvena Multiplication
Comparative Analysis of Multiplication Methods
Technique | Best Use | Complexity |
---|---|---|
Nikhilam | Numbers close to base 10 | Low |
Urdhva-Tiryagbhyam | Multi-digit numbers | Medium |
Ekanyunena Purvena | Multiplying by 9s | Low |
When to Use Fast Multiplication
Choosing the right method for multiplying depends on the numbers you’re working with. Mental calculation skills get better with practice, making math problems easier to solve4. Learning these quick math tricks can really help students9.
The art of quick multiplication lies not just in knowing techniques, but in understanding their application.
Using Vedic Mathematics can make you faster and more confident in math9.
Multiplication Tips for Students
Learning mental math techniques can change how students solve math problems. Our method makes multiplication fun and easy with new learning ways.

Students can get better at quick math by practicing the right way. Studies show many ways to boost math skills.
Engaging Learning Techniques
To get good at multiplication, we need fun and hands-on methods. Here are some great ways to learn:
- Gamify math to make it fun
- Use visual tools to help understand
- Learn tricks that fit your learning style10
“Vedic Mathematics is easier to learn, faster to use and less prone to error than conventional methods.” – Dr. Michael Weinless
Practice Strategies for Mastery
Good multiplication learning needs regular practice. The Urdhva Tiryagbhyam Sutra is a great tool for quick math11. Here are some practice tips:
- Break down hard multiplications into smaller steps12
- Try vertical and crosswise methods
- Practice problems that get harder as you go
Remember, regular practice is key. By spending time on mental math, students can get really good at math10.
Worksheet Recommendations
Make worksheets that get harder as you go. Start with simple problems and add more complexity to build confidence.
Using these tips, students can improve their math skills. This makes math fun and easy to learn.
Real-Life Applications of Multiplication Tricks
Multiplication tricks are not just for school. They change how we solve problems in work and life. Fast and easy ways to multiply have made solving problems better in many areas.
Vedic Mathematics shows how new math ideas can help a lot13. These ideas are useful in many fields, from simple tasks to complex tech areas.
Multiplication in Everyday Life
Quick ways to multiply make daily math easier. Here are some examples:
- Fast mental math for money matters
- Quick time calculations
- Scaling recipes in cooking
- Planning budgets for shopping
The Urdhva-Tiryak Sutra makes math faster13. It lets people solve hard math problems quickly, without needing calculators.
Applications in Technology and Engineering
Fast multiplication algorithms are key in tech. Vedic Mathematics is useful in:
- Computer science
- Engineering
- Optimizing data processing
- Doing well in exams13
Vedic Mathematics makes hard math easy and fast13.
These math tricks are useful in many areas, like IIT-JEE, SAT, and CAT13. Learning these methods helps people solve math problems faster and more accurately.
Advanced Urdhva Tiryagbhyam Techniques
Vedic mathematics brings advanced ways to solve tough multiplication problems. We’ll explore advanced urdhva tiryagbhyam sutra techniques. These will help researchers and students solve complex math problems14.
Combining Techniques for Complex Problems
For solving tough math problems, we need new ideas. The urdhva tiryagbhyam sutra is great for solving hard multiplication problems14. It helps make complex math easier for everyone.
- Works well with big numbers
- Makes math simpler
- Speeds up math work
Mastering Multi-Digit Multiplication
Using vedic math makes multiplying big numbers easy. The Urdhva-Tiryak Sutra has a general formula for all multiplication14. This means researchers can solve hard math problems fast and accurately.
Technique | Digit Range | Complexity Level |
---|---|---|
Basic Vertical Crosswise | 2-3 digits | Beginner |
Advanced Urdhva Method | 4-8 digits | Intermediate |
Complex Multiplication | 9+ digits | Advanced |
Vedic math makes hard math easy and simple.
Learning these advanced methods boosts your math skills. By using strategic learning, you can solve math problems better15.
Resources for Further Learning
Learning multiplication tricks and mental math techniques needs good resources. Our guide will show you top materials to improve your math skills and boost your brain.
Recommended Books for Multiplication Mastery
Vedic Mathematics has many learning resources. It has books that go deep into multiplication methods16:
- “A Handbook on Vedic Mathematics” (77 pages)
- “A Modern Introduction to Ancient Indian Mathematics” (272 pages)
- “All You Wanted to Know About Vedic Mathematics” (144 pages)
Online Courses and Digital Learning Platforms
Digital platforms have changed how we learn multiplication tricks. Vedic Mathematics covers many math areas, like arithmetic and calculus3. These online tools offer fun ways to learn mental math.
Resource Type | Key Features |
---|---|
Online Courses | Interactive video lessons, practice modules |
Mobile Apps | Real-time calculation practice, skill tracking |
Webinars | Expert-led sessions, live problem-solving |
Practice Tools and Applications
Practice tools can really help improve your math skills. Studies show Vedic methods can make solving problems faster by 50% and cut down errors by 30%7.
“The art of mathematics is not about memorization, but understanding the underlying principles.” – Vedic Mathematics Principle
Using these resources, you can change how you do multiplication and mental math. You’ll reach new heights in numbers.
Case Studies: Success Stories
Speedy calculations have changed lives in amazing ways. We’ve looked into how Vedic Mathematics has helped people become math experts. These stories show how powerful these methods can be.
Educators’ Insights into Mathematical Mastery
Teachers all over the world have seen big changes with Vedic Mathematics. Dhaval Bathia, a well-known educator, has changed how math is taught. His methods have been praised for boosting students’ math skills17.
Student Testimonials: Breakthrough Experiences
Students who use Vedic Mathematics have seen big improvements. They say they can solve problems faster and feel more confident in math. Here are some key points:
- Increased computational speed
- Enhanced problem-solving skills
- Reduced mathematical anxiety
“Vedic Mathematics transformed my approach to numbers, making calculations feel like an enjoyable puzzle rather than a challenging task.”
Professional Applications and Impact
Vedic Mathematics is not just for school. It’s also used in the workplace. People have seen their math skills improve by up to 25%7. It’s great for exams and technical jobs7.
Learning Milestones and Achievements
Studies show Vedic Mathematics can really help. Students have seen their test scores go up by 20%7. It also cuts down on math mistakes by about 30%7.
These stories show how powerful math can be. They encourage everyone to try new ways of learning math.
Conclusion: The Future of Multiplication Mastery
Multiplication tricks and Vedic mathematics are leading the way in education. They can change how we learn math for everyone18.
Vedic math goes beyond just solving problems. A big survey found that 90% of students like using these methods in class18. By mixing old wisdom with new tech, we can make learning fun and easy19.
Tools like LabVIEW are already making math lessons better18. Vedic math has 16 main rules and 13 sub-rules. These help simplify hard math problems18. They help students feel less stressed and solve problems better.
Embracing Modern Learning Tools
The future of mastering multiplication is combining old methods with new tech. By keeping up with these changes, we can understand numbers better and solve problems faster.
The Importance of Continued Learning in Mathematics
Learning math never stops. Those who keep exploring and trying new things will lead in math. They will have tools that go beyond just solving problems.
FAQ
What is the Urdhva Tiryagbhyam Sutra?
How do multiplication tricks differ from traditional calculation methods?
Are Vedic multiplication techniques suitable for complex mathematical operations?
Can anyone learn Vedic multiplication techniques?
What are the practical applications of Vedic multiplication techniques?
How long does it take to become proficient in Urdhva Tiryagbhyam multiplication?
Are there digital resources available for learning Vedic multiplication?
How do Vedic multiplication techniques compare to modern computational methods?
Source Links
- https://www.thevedicmaths.com/post/vedic-maths-for-multiplication
- http://www.vedamu.org/veda/1795$vedic_mathematics_methods.pdf
- https://www.geeksforgeeks.org/vedic-maths/
- https://www.geeksforgeeks.org/best-shortcut-tricks-of-multiplication/
- https://swaadhi.com/learning-vedic-maths/
- https://www.pixelirk.com/tech/2023/07/21/vedic-math-and-vedic-geometry-ancient-techniques-for-modern-mathematics/
- https://www.abhijeetshirke.in/vedic-mathematics/
- https://promathm.wordpress.com/2020/05/20/what-is-vedic-mathematics/
- https://www.orchidsinternationalschool.com/blog/what-is-vedic-maths
- https://vedicmathschool.org/question/
- https://www.theproblemsite.com/lesson-plans/math/mental-math/vedic/easy-and-fast-multiplication
- https://www.justquant.com/fast-math-tricks/multiplication-by-3-digit-numbers-vedic-math-tricks/
- https://mathgiri.com/introduction-to-vedic-mathematics-the-ancient-indian-math-system/
- https://www.elixirpublishers.com/articles/1685778835_201110012.pdf
- http://www.rget.co.in/dev/course/252
- https://www.vedicmaths.org/resources/books/other-books
- https://www.rljdmcdavpselibrary.com/books/vedicmaths.pdf
- https://www.academia.edu/5155374/Vedic_Mathematics_Methods
- https://www.slideshare.net/slideshow/vedic-ppt/16875493