Methods and practice of quick calculation of addition, multiplication, division, square and square root of numbers through Vedic mathematics

Vedic Mathematics is an ancient Indian system of calculation derived from the Vedas, particularly the Atharva Veda. Rediscovered and systematized by Bharati Krishna Tirthaji in the early 20th century, it consists of 16 sutras (formulas) and 13 sub-sutras (sub-formulas) that provide quick and efficient methods for mathematical operations. These techniques cover arithmetic, algebra, geometry, calculus, and more.

At its core, Vedic Mathematics emphasizes mental calculation, pattern recognition, and logical simplicity. Unlike conventional methods, it allows solving problems from left to right, encourages the use of estimation, and reduces lengthy steps through smart shortcuts. For instance, complex multiplication, division, squaring, and even extracting roots can be done mentally with remarkable speed and accuracy.

Vedic Mathematics is particularly beneficial in education, helping students overcome math anxiety, enhance concentration, and improve problem-solving skills. It also finds practical applications in competitive exams, business, banking, and everyday life.

In the modern context, it bridges traditional wisdom and contemporary needs, making it both a heritage tool and a futuristic skill. With its universal applicability and efficiency, Vedic Mathematics stands as a timeless and holistic approach to mastering numbers and fostering analytical thinking.

1. Quick Addition using Vedic Mathematics

Method: Left-to-Right Addition (Place Value Method)

In Vedic Mathematics, addition is done from left to right (unlike the traditional right-to-left method), improving speed and mental calculation.

Technique:

Break numbers into place values and add them part-by-part.

Example:

Add 467 + 385
Break into hundreds, tens, and units:

• 400 + 300 = 700

• 60 + 80 = 140

• 7 + 5 = 12
  Now add:
  700 + 140 = 840
  840 + 12 = 852

This technique builds mental strength and accuracy.

2. Quick Multiplication using Vedic Mathematics

Method 1: Vertically and Crosswise (Urdhva–Tiryagbhyam Sutra)

Applies to general multiplication, even for large numbers.

Example:

Multiply 23 × 14
Step 1: Units digit → 3 × 4 = 12 (write 2, carry 1)
Step 2: Cross multiplication + addition → (2×4 + 3×1) = 8 + 3 = 11 (+1 carry = 12; write 2, carry 1)
Step 3: Tens digit → 2 × 1 = 2 (+1 carry = 3)
So, the answer is 322

Method 2: Base Method (Nikhilam Sutra)

Use when numbers are near base values (10, 100, 1000).

Example:

Multiply 97 × 96 (Base = 100)
Step 1: 97 is 3 less → -3; 96 is 4 less → -4
Step 2: Cross subtract: 97 – 4 = 93 or 96 – 3 = 93
Step 3: Multiply deviations: 3 × 4 = 12
Answer: 9312

3. Quick Division using Vedic Mathematics

Method: Paravartya Yojayet Sutra (Transpose and Adjust)

Use when the divisor is near powers of 10.

Example:

Divide 1125 by 9

Step 1: Divide 1 (first digit of 1125) by 9 → 0 remainder 1

Step 2: Bring down the next digit (1), making 11.

11 ÷ 9 = 1 remainder 2

Bring down 2 → 22

22 ÷ 9 = 2 remainder 4

Bring down 5 → 45 ÷ 9 = 5

Answer: 125

Short Division with Remainders:

Use recurring decimals or express in quotient + remainder form. Vedic division saves long steps and enables mental practice.

4. Quick Square using Vedic Mathematics

Method 1: Squaring Numbers Ending in 5 (Ekadhikena Purvena Sutra)

Example:

Find the square of 85

Step 1: Split 85 → 8 and 5

Step 2: Multiply 8 × 9 = 72

Step 3: Always append 25 at the end → 7225

So, 85² = 7225

Method 2: For Numbers Close to Base

Example:

Square of 96 (Base 100, deviation = -4)
Step 1: 96 – 4 = 92
Step 2: Square of 4 = 16
Answer: 9216

This method applies for any number near 100, 1000, etc.

5. Quick Square Root using Vedic Mathematics

Method: Visual Estimation + Place Value Logic

Step 1: Look at the last digit of the number and determine possible root endings.
Step 2: Find the nearest square less than the number.
Step 3: Use logic and approximation.

Example:

Find √4489

Step 1: 60² = 3600, 70² = 4900 → So, root lies between 60 and 70

Step 2: Try 67² = 4489

Answer: √4489 = 67

Vedic method uses pattern recognition and mental estimation, not trial and error.

Practice Tips:

• Use mental exercises daily with 2-digit and 3-digit numbers.

• Write and compare both conventional and Vedic methods.

• Apply Vedic tricks in real-life scenarios (billing, shopping, budgeting).

• Focus on base values (10, 100, 1000) for faster speed in multiplication and division.

• Practice left-to-right computation for better visualization.