Vedic Math Tricks for Competitive Exams — The Complete 2026 Guide

Vedic Mathematics is a system of mental calculation derived from ancient Indian scriptures called the Vedas. Rediscovered and compiled by Bharati Krishna Tirthaji in the early 20th century, it consists of 16 main sutras (formulas) and 13 sub-sutras that cover virtually every branch of arithmetic and algebra.

What makes Vedic Math exceptionally relevant for competitive exams is not its ancient origins — it is its extraordinary efficiency. Vedic techniques routinely solve problems in one-third the steps required by conventional methods. For an SSC CGL or RRB NTPC candidate sitting in an exam hall without a calculator, this difference translates directly into extra time, higher accuracy, and better scores.

This guide covers the most exam-relevant Vedic Math techniques with complete worked examples, practical applications, and specific guidance on where each technique appears in competitive examinations.

The 16 Vedic Math Sutras — A Quick Overview

Each sutra is a short Sanskrit phrase that encodes a mathematical principle. You do not need to memorize the Sanskrit — understanding the principle and its application is what matters.

In this guide we focus on the six sutras with the highest direct exam relevance.

Sutra 1: Ekadhikena Purvena — Squaring Numbers Ending in 5

Translation: "By one more than the previous one"

This is the sutra behind the "numbers ending in 5" squaring trick. It is the most widely known Vedic Math technique and the fastest entry point into the system.

The Method:

• Take the digit(s) before 5
• Multiply by itself plus 1
• Append 25

Worked Examples:

• 25² → 2 × 3 = 6 → 625
• 45² → 4 × 5 = 20 → 2025
• 75² → 7 × 8 = 56 → 5625
• 115² → 11 × 12 = 132 → 13225
• 145² → 14 × 15 = 210 → 21025

Exam application: Appears in simplification, number series, and geometry questions where side lengths end in 5.

Sutra 2: Nikhilam — Multiplication Near Base Numbers

Translation: "All from 9 and the last from 10"

This is the most powerful Vedic multiplication sutra and the one with the broadest exam application. It handles multiplication of numbers near any base — 10, 100, 1000, or multiples thereof.

Case 1: Both Numbers Below the Base (100)

Method:

1. Find the deficit of each number from 100
2. Cross-subtract: take either number minus the other's deficit
3. Multiply the two deficits for the right part (use 2 digits)
4. Combine

Worked Examples:

97 × 96:

• Deficits: 3 and 4
• Cross: 97 − 4 = 93 (or 96 − 3 = 93)
• Right part: 3 × 4 = 12
• Answer: 9312

88 × 97:

• Deficits: 12 and 3
• Cross: 88 − 3 = 85
• Right part: 12 × 3 = 36
• Answer: 8536

86 × 94:

• Deficits: 14 and 6
• Cross: 86 − 6 = 80
• Right part: 14 × 6 = 84
• Answer: 8084

78 × 89:

• Deficits: 22 and 11
• Cross: 78 − 11 = 67
• Right part: 22 × 11 = 242 → carries into left part: 67 + 2 = 69, right = 42
• Answer: 6942

Case 2: Both Numbers Above the Base (100)

When numbers exceed the base, use surpluses instead of deficits. Add instead of subtract.

103 × 107:

• Surpluses: 3 and 7
• Cross: 103 + 7 = 110 (or 107 + 3 = 110)
• Right part: 3 × 7 = 21
• Answer: 11021

112 × 108:

• Surpluses: 12 and 8
• Cross: 112 + 8 = 120
• Right part: 12 × 8 = 96
• Answer: 12096

Case 3: One Above, One Below the Base

103 × 97:

• 103 surplus = +3, 97 deficit = −3
• Cross: 103 − 3 = 100 (or 97 + 3 = 100)
• Right part: (+3) × (−3) = −9 → 100 × 100 − 9 = 9991

107 × 94:

• Surplus: +7, Deficit: −6
• Cross: 107 − 6 = 101
• Right part: 7 × (−6) = −42 → 10100 − 42 = 10058

Using Base 10 and Base 1000

Base 10 — 7 × 8:

• Deficits: 3 and 2
• Cross: 7 − 2 = 5
• Right part: 3 × 2 = 6 (1 digit for base 10)
• Answer: 56

Base 1000 — 997 × 994:

• Deficits: 3 and 6
• Cross: 997 − 6 = 991
• Right part: 3 × 6 = 018 (3 digits for base 1000)
• Answer: 991018

Sutra 3: Urdhva Tiryagbhyam — General Multiplication

Translation: "Vertically and crosswise"

This is the universal Vedic multiplication sutra — it works for any two numbers regardless of their proximity to a base. For competitive exams, it is the fastest method for multiplying two 2-digit numbers.

Multiplying Two 2-Digit Numbers (AB × CD)

The method produces three components:

• Right digit: B × D
• Middle digit: (A × D) + (B × C)
• Left digit: A × C

Add carries from right to left.

Example 1: 32 × 41

• Right: 2 × 1 = 2
• Middle: (3×1) + (2×4) = 3 + 8 = 11 → write 1, carry 1
• Left: 3 × 4 = 12 + 1 = 13
• Answer: 1312

Example 2: 54 × 67

• Right: 4 × 7 = 28 → write 8, carry 2
• Middle: (5×7) + (4×6) = 35 + 24 = 59 + 2 = 61 → write 1, carry 6
• Left: 5 × 6 = 30 + 6 = 36
• Answer: 3618

Example 3: 78 × 93

• Right: 8 × 3 = 24 → write 4, carry 2
• Middle: (7×3) + (8×9) = 21 + 72 = 93 + 2 = 95 → write 5, carry 9
• Left: 7 × 9 = 63 + 9 = 72
• Answer: 7254

Extending to 3-Digit Numbers

For ABC × DEF, the method extends to five components. For exam purposes, the 2-digit version handles the vast majority of cases — practice this until it runs in under 6 seconds.

Sutra 4: Paravartya Yojayet — Fast Division

Translation: "Transpose and apply"

This sutra provides a fast method for dividing by numbers close to a power of 10.

Dividing by Numbers Near 10 (like 9, 11, 12)

Division by 9 — The Pattern Method:

For any number divided by 9, there is a direct pattern:

• Write the first digit as the first quotient digit
• Add each subsequent digit to the running quotient for the next quotient digit
• The final sum (if less than 9) is the remainder

Example: 1234 ÷ 9

• First quotient digit: 1
• 1 + 2 = 3 → second quotient digit: 3
• 3 + 3 = 6 → third quotient digit: 6
• 6 + 4 = 10 → remainder: 10, so add 1 to quotient → quotient = 137, remainder = 1
• Answer: 137 remainder 1 → verify: 137 × 9 + 1 = 1233 + 1 = 1234 ✓

Example: 2341 ÷ 9

• 2 → 2+3=5 → 5+4=9 → 9+1=10
• Quotient: 260, remainder: 1
• Answer: 260 r 1

Sutra 5: Yavadunam — Squaring Numbers Near a Base

Translation: "Whatever the deficiency, lessen it still further by that amount and set up the square of the deficiency"

This sutra squares numbers near any base with remarkable speed.

Squaring Near 100

Method:

1. Find how far the number is from 100 (d = deficit or surplus)
2. Left part: number + d (or number − d if below base)
3. Right part: d² (always 2 digits)

Examples — Below 100:

96²:

• d = −4
• Left: 96 − 4 = 92
• Right: 4² = 16
• Answer: 9216

93²:

• d = −7
• Left: 93 − 7 = 86
• Right: 7² = 49
• Answer: 8649

88²:

• d = −12
• Left: 88 − 12 = 76
• Right: 12² = 144 → carry 1 → Left = 77, Right = 44
• Answer: 7744

Examples — Above 100:

104²:

• d = +4
• Left: 104 + 4 = 108
• Right: 4² = 16
• Answer: 10816

112²:

• d = +12
• Left: 112 + 12 = 124
• Right: 12² = 144 → carry 1 → Left = 125, Right = 44
• Answer: 12544

Squaring Near 50

Method: Use base 50 = 100/2

Example: 47²

• d = −3 from 50
• Left: 47 − 3 = 44, then divide by 2: wait — adjusted method:
• Left part = (50 + d)²/100 approach → simpler: use (50−3)² = 2500 − 300 + 9 = 2209

Example: 53²:

• (50+3)² = 2500 + 300 + 9 = 2809

Sutra 6: Ekanyunena Purvena — Multiplying by a Series of 9s

Translation: "By one less than the previous one"

This sutra handles multiplication by 9, 99, 999, and any number consisting entirely of 9s.

Multiplying by 9:
N × 9 = N × (10−1) = 10N − N

Multiplying by 99:
N × 99 = N × (100−1) = 100N − N

Multiplying by 999:
N × 999 = 1000N − N

Worked Examples:

• 47 × 99 = 4700 − 47 = 4653
• 83 × 999 = 83,000 − 83 = 82,917
• 246 × 99 = 24,600 − 246 = 24,354
• 37 × 999 = 37,000 − 37 = 36,963
• 125 × 9999 = 1,250,000 − 125 = 1,249,875

Exam application: This appears frequently in simplification questions and is one of the fastest calculation shortcuts available.

Vedic Math for Cube Roots and Square Roots

Instant Square Roots of Perfect Squares

For perfect squares up to 10,000, Vedic Math provides a two-step method.

Method:

1. The last digit of the root is determined by the last digit of the square (use the table below)
2. The first digit is found by identifying which perfect square the remaining left digits fall between

Last digit mapping:

Example: √7056

• Last digit: 6 → root ends in 4 or 6
• Remaining: 70 → falls between 8²=64 and 9²=81 → first digit = 8
• Candidates: 84 or 86
• Check: 84² = 7056 ✓ → Answer: 84

Example: √5329

• Last digit: 9 → root ends in 3 or 7
• Remaining: 53 → falls between 7²=49 and 8²=64 → first digit = 7
• Candidates: 73 or 77
• Check: 73² = 5329 ✓ → Answer: 73

Applying Vedic Math in Competitive Exams — Quick Reference

A 3-Week Vedic Math Learning Plan

Practice principle: Learn one sutra completely before moving to the next. Partial knowledge of six sutras is less useful than complete fluency in three.