Vedic Maths Trick, Method and Sutras for Speed

Vedic Maths is an ancient system of mathematics rooted in the Indian Vedas, specifically the Atharva Veda.

It simplifies complex mathematical operations using unique techniques that make the problem more manageable and easier to calculate mentally with formulas known as the sutras. These methods provide fast, efficient, and innovative ways to solve problems that traditionally require lengthy calculations.

With a surge in global interest in improving mental math skills, Vedic Maths is now a preferred choice for students, educators, and professionals.

Its versatility and ability to break down intimidating problems make it much easier to do it just mentally with a little practice and experience. Now let’s look at some of the most amazing tricks in Vedic Maths!

Table of Contents

Vedic Math Trick 1: Calculate the Square of Any Number that Ends with 5 in Seconds

If you are curious like me and want to find out more about these amazing methods in detail, make sure that you check out our video tutorial on, how we can find the square of any number near base 50.

Vedic Maths Shortcut to Find Square of any Number | 1-1000 Square निकालें सिर्फ 5 सेकंड में | Part 1

This method works exclusively for numbers ending in 5. Here’s a concise three-step process to find the square:

Example: Find the square of 65

Step 1: Square the digit at the unit place (5): 5² = 25. Keep “25” aside.

Step 2: Take the number left of 5 (6). Add 1 to it (6 + 1 = 7), then multiply the result by the original number (6 × 7 = 42).

Step 3: Combine the results from Steps 1 and 2: 42 (from Step 2) + 25 (from Step 1) = 4225.

More Examples:

Example 1: Square of 85

5² = 25
8 + 1 = 9; 8 × 9 = 72
Combine: 7225

Example 2: Square of 155

5² = 25
15 + 1 = 16; 15 × 16 = 240
Combine: 24025

Practice Questions

145^2=?
215^2=?
75^2=?
85^2=?
(5.35)^2=?
195^2=?
85^2=?
995^2=?

Vedic Math Trick 2: Multiply Numbers Close to the Base of 10 in Seconds

Nikhilam Sutra, or “all from 9 and the last from 10,” is a quick multiplication technique that works best when numbers are close to a base like 10, 100, or 1000. Here is the video tutorial for you:

Nikheluam Method Of Multiplication by Vedic Math School

Understand the Process

Here’s a simple three-step process:

Example: Multiply 98 × 97

Step 1: Find the deviations from the base. For 98 and 97 (base 100):

98 is 2 less than 100 (– 2).
97 is 3 less than 100 (– 3).

Step 2: Multiply the deviations: (– 2) × (– 3) = 6.

Step 3: Subtract the cross-deviation from the base number:

Take one number (98) and subtract the other number’s deviation (3): 98 – 3 = 95.
Combine the results: 9500 + 6 = 9506.

More Examples:

Example 1: Multiply 89 × 97 (Base 100)

Deviations: 89 (– 11), 97 (– 3)
Multiply deviations: (– 11) × (– 3) = 33
Subtract cross-deviation: 89 – 3 = 86
Combine: 8600 + 33 = 8633

Example 2: Multiply 102 × 104 (Base 100)

Deviations: 102 (+2), 104 (+4)
Multiply deviations: 2 × 4 = 8
Add cross-deviation: 102 + 4 = 106
Combine: 10600 + 8 = 10608

This technique is perfect for quick mental calculations when numbers are near common bases like 10, 100, or 1000.

Practice Question

Find the solution of the following:

97 × 98=?
102 × 104=?
89 × 96=?
105 × 99=?
995 × 997=?
110 × 95=?

Vedic Math Trick 3: Verify Your Answers While Adding or Multiplying in Seconds

The Digit Sum technique simplifies calculations and checks the correctness of operations by reducing numbers to a single digit.

Here is the video tutorial for you:

How to Verify your Answer? Right and Wrong | Vedic Check System and Digital Roots: Vedic Math School

Step by step Process to do Multiplication:

Here’s a concise guide:

Example: Find the Digit Sum of 468

Step 1: Add all digits of the number: 4 + 6 + 8 = 18.

Step 2: If the result is a multi-digit number, add its digits again: 1 + 8 = 9.

Step 3: The single-digit result is the digit sum: 9.

How to Use Digit Sum:

1. Verification of Multiplication:

Example 1: Check if 21 × 14 = 294.

Find the digit sums:

For 21: 2 + 1 = 3
For 14: 1 + 4 = 5

Multiply the digit sums: 3 × 5 = 15 → 1 + 5 = 6

Find the digit sum of the result (294):

2 + 9 + 4 = 15 → 1 + 5 = 6

Both match, so the calculation is likely correct.

Example 2: Check if 26 × 35 = 910.

Find the digit sums:

For 26: 2 + 6 = 8
For 35: 3 + 5 = 8

Multiply the digit sums: 8 × 8 = 64 → 6 + 4 = 10 → 1 + 0 = 1

Find the digit sum of the result (910):

9 + 1 + 0 = 10 → 1 + 0 = 1

Both match, so the calculation is likely correct.

2. Simplifying Large Numbers:

Example: Find the digit sum of 987654.
Add digits: 9 + 8 + 7 + 6 + 5 + 4 = 39 → 3 + 9 = 12 → 1 + 2 = 3.
Digit sum: 3.

More Examples:

Example 1:

Digit Sum of 256 = 2 + 5 + 6 = 13 → 1 + 3 = 4

Example 2:

Digit Sum of 789 = 7 + 8 + 9 = 24 → 2 + 4 = 6

3. Verification for Addition

Example 1: Check if 21 + 14 = 35.

Find the digit sums:

For 21: 2 + 1 = 3
For 14: 1 + 4 = 5

Add the digit sums: 3 + 5 = 8

Find the digit sum of the result (35):

3 + 5 = 8

Both match, so the calculation is likely correct.

Example 2: Check if 26 + 35 = 61.

Find the digit sums:

For 26: 2 + 6 = 8
For 35: 3 + 5 = 8

Add the digit sums: 8 + 8 = 16 → 1 + 6 = 7

Find the digit sum of the result (61):

6 + 1 = 7

Both match, so the calculation is likely correct.

Digit Sum for Checking Multiplication:

Digit sum is preserved in multiplication, meaning the digit sum of the product equals the digit sum of the multiplier and multiplicand multiplied together.

Example 1: Check if 21 × 14 = 294.

Find digit sums: 21 → 2 + 1 = 3, 14 → 1 + 4 = 5.

Multiply digit sums: 3 × 5 = 15 → 1 + 5 = 6.

Digit sum of 294: 2 + 9 + 4 = 15 → 1 + 5 = 6.

Both match, confirming the calculation.

Example 2: Check if 36 × 48 = 1728.

Find digit sums: 36 → 3 + 6 = 9, 48 → 4 + 8 = 12 → 1 + 2 = 3.

Multiply digit sums: 9 × 3 = 27 → 2 + 7 = 9.

Digit sum of 1728: 1 + 7 + 2 + 8 = 18 → 1 + 8 = 9.

Both match, so the result is correct.

Shortcut: Casting Out Nines

To speed up digit sum calculations, “cast out” any 9s or pairs adding to 9 from the number.
Example: For 987654, cast out 9 and pair 8+1, 7+2, and 6+3, leaving only 0, digit sum = 0.

Practice Questions for Verifying Using the Digit Sum Technique

Verify if 56 × 34 = 1904 using the digit sum method.
Check if 123 × 45 = 5535 by finding the digit sums of all numbers involved.
Verify if 78 + 96 = 174 using the digit sum technique.
Check if 432 × 21 = 9072 by comparing the digit sums.
Use the digit sum method to confirm if 89 × 32 = 2848.
Verify if 67 + 89 = 156 using the rules of the digit sum system.

Vedic Math Trick 4: Multiply Any Two or Three-Digit Numbers in Seconds

The Urdhva-Tiryagbyham Sutra simplifies the multiplication of numbers vertically and crosswise. It’s applicable for two- or three-digit numbers. For a more detailed explanation, make sure that you check out our dedicated tutorial on Urdhva-Tiryagbyham Sutra:

Vedic Maths Multiplication Special Tricks | दो और तीन अंकों का Multiplication आसानी से 2 Second में

Example: Multiply 23 × 45

Step 1: Multiply the unit digits: 3 × 5 = 15. Write 5 and carry over 1.

Step 2: Cross-multiply and add: (2 × 5) + (3 × 4) = 10 + 12 = 22. Add the carry (1): 22 + 1 = 23. Write 3 and carry over 2.

Step 3: Multiply the tens digits: 2 × 4 = 8. Add the carry (2): 8 + 2 = 10.

Combine the results: 1035.

Example: Multiply 123 × 456

Step 1: Multiply the unit digits: 3 × 6 = 18. Write 8 and carry over 1.

Step 2: Cross-multiply adjacent digits and add: (2 × 6) + (3 × 5) = 12 + 15 = 27. Add the carry (1): 27 + 1 = 28. Write 8 and carry over 2.

Step 3: Multiply diagonally and add: (1 × 6) + (2 × 5) + (3 × 4) = 6 + 10 + 12 = 28. Add the carry (2): 28 + 2 = 30. Write 0 and carry over 3.

Step 4: Multiply the hundreds of digits: 1 × 4 = 4. Add the carry (3): 4 + 3 = 7.

Combine the results: 56088.

More Examples:

Example 1: Multiply 34 × 56

Units: 4 × 6 = 24. Write 4, carry 2.
Crosswise: (3 × 6) + (4 × 5) = 18 + 20 = 38. Add carry: 38 + 2 = 40. Write 0, carry 4.
Tens: 3 × 5 = 15. Add carry: 15 + 4 = 19.
Result: 1904.

Example 2: Multiply 112 × 321

Units: 2 × 1 = 2.
Crosswise 1: (1 × 1) + (2 × 2) = 1 + 4 = 5.
Crosswise 2: (1 × 2) + (1 × 3) + (1 × 1) = 2 + 3 + 1 = 6.
Hundreds: 1 × 3 = 3.
Result: 35952.

Urdhva-Tiryagbyham is just one sutra of 16, Sri Bharati Krishna Tirthaji Maharaja gave us 16 Sutras, which became a pillar for Vedic Maths.

Practice Problem for Two-Digit Multiplication

43 X 21=?
32 X 45=?
23 X 46=?
32 X 21=?
32 X 45=?
43 X 21=?

Practice Problem for Three-Digit Multiplication

324 X 231=?
415 X 326=?
234 X 312=?
654 X 234=?
789 X 654=?
324 X 423=?

How to Start Learning Vedic Math

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Vedic Math is an ancient system that transforms complex calculations into effortless mental exercises. Tricks like squaring numbers ending in 5 and verifying answers with digit sums enhance speed, accuracy, and confidence. These methods are simple yet powerful, helping students and professionals alike conquer math with ease. Ready to sharpen your skills? For more information about what we do, make sure that you check out our YouTube channel.

At Vedic Math School, we offer practical, structured courses designed for students, teachers, and professionals. Whether you’re looking to tackle competitive exams, sharpen your mental math skills, or make day-to-day calculations quicker, our proven Vedic Maths techniques have you covered. With step-by-step guidance and real-world applications, learning becomes easier and more efficient.

Vedic Maths Trick, Method and Sutras for Speed