Home ยป 10 Mind-Blowing Vedic Math Tricks for Competitive Exams

10 Mind-Blowing Vedic Math Tricks for Competitive Exams

Update on: 10 Feb 2025, 05:45 PM

Do you always struggle while solving complex math calculations in various competitive exams? Do you waste a lot of time while dealing with lengthy calculations? In this blog, we will try to make your calculations less time-consuming and more precise by applying the power of 10 amazing Vedic Math tricks. These tricks can play a humongous role in your competitive exams.

  1. Squaring of Number Ending in 5

The following steps are involved in the squaring process:

Step 1: The square of the given number has two parts โ€“ LHP and RHP.

Step 2: RHP = Square of ones digit.

Step 3: LHP = Product of the number formed by the remaining digits and its successor.

Step 4: Write LHP and RHP together as answer.

Question: Find the square of 155

Answer: (155)2 = 15 ร— (15 +1) | 52

ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย  = 240 | 25

ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย  = 24025

Must Check – 10 Vedic Maths Tricks For Rapid Calculations

  1. Square of 2-Digit Numbers not Ending in 5

Step 1: The square consists of three parts โ€“ LHP, Middle Part and RHP

Step 2: LHP = Square of digit at units place.

Step 3: RHP = Square of the digit at units place.

Step 4: Middle part = 2 times the product of the two digits of the number to be squared.

Step 5: If RHP consists of two digit, the digit at tens place is carried over to middle part and added to it. Similarly from middle part to LHP.

Question: Find the square of 29

Answer: (29)2 = 22ย ย  | 2ย  ร— 2 ร— 9 | 92ย 

ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย  = 4 | 36 | 81

ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย  = 4 | 36 + 8 = 44 | 1

ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย  = 4+4 | 4 | 1

ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย  = 8 | 4 | 1

ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย  = 841

  1. Square of 3-Digit Numbers not Ending in 5

Step 1: LHP = Add the difference of the number and the working base, to the given number.

Step 2: RHP = Square of the difference of the number and the base.

Step 3: Multiply LHP by first digit of working base.

Step 4: RHP must contain two digits. If RHP consists of only digit, then put a zero before it. If RHP consists of three or more digits then the number formed by hundreds, thousands..place digits are carried over to LHP and added to it.

Step 5: Write both LHP and RHP together as the answer.

Question: Find the square of 716

Answer: (716)2 = 716 + (716-700) | (716 โ€“ 700)2

ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย  ย ย ย ย ย ย ย = 716 + 16 | (16)2

ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย  = 732 ร— 7 | 256

ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย  = 5124 + 2 | 56

ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย  = 512656

  1. Square of Numbers when Base is 100 and Below and Nearer to the Base

Step 1: Take the nearest power of 100 as base and find the deficit (= Base โ€“ Number).

Step 2: Obtain the left-hand part (LHP) of answer by decreasing the number by its deficit.

Step 3: Obtain the right-hand part (RHP) of answer by squaring the deficit of the number.

Step 4: If LHP is negative, add it to the carried over number from RHP (This depends on the number of digits in the base).

Question: Find the square of 91

Answer: 912ย ย  = 91 โ€“ (100-91) | (100-91)2ย 

ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย  ย ย ย ย ย ย ย ย ย  = 91 โ€“ 9 | 92

ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย  ย ย ย ย ย ย ย ย ย  = 8281

  1. Square of Numbers when Base is 100 and Above and Nearer to the Base

Step 1: Take the nearest power of 100 as base and find the surplus (= Number – Base).

Step 2: Obtain the left-hand part (LHP) of answer by decreasing the number by its surplus.

Step 3: Obtain the right-hand part (RHP) of answer by squaring the surplus of the number.

Step 4: If LHP is negative, add it to the carried over number from RHP (This depends on the number of digits in the base).

Question: Find the square of 105

Answer: 1052ย ย  = 105 + (105-100) | (105-100)2ย 

ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย  ย ย ย ย ย ย ย ย ย  = 105 + 5 | 52

ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย  ย ย ย ย ย ย ย ย ย  = 110 | 25

ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย  ย ย ย ย ย ย ย ย ย  = 11025

  1. Square of Numbers when Base is 1000 and Nearer to High Base

Step 1: Take the nearest power of 1000 as base and find the deficit (= Base โ€“ Number).

Step 2: Obtain the left-hand part (LHP) of answer by decreasing the number by its deficit.

Step 3: Obtain the right-hand part (RHP) of answer by squaring the deficit of the number.

Step 4: If LHP is negative, add it to the carried over number from RHP (This depends on the number of digits in the base).

Question: Find the square of 983

Answer: 9832ย  = 983 โ€“ (1000 โ€“ 983) | (1000 – 983)2

ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย  ย ย ย ย ย ย ย ย ย ย  = 983 โ€“ 17 | 172

ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย  ย ย ย ย ย ย ย ย ย ย  = 966 | 289

ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย  = 966289

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  1. Multiplication by 50

To multiply any number by 50, convert it to the nearest base i.e., 100 by multiplying it by 2. Then divide the product by 2.

Question: Multiply 289 by 50

Answer: 289 ร— 50 = (289 ร— 50 ร— 2) / 2

ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย  = (289 ร— 100) 2

ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย  = 28900/2

ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย  = 14450

ย 

  1. Multiplication by 25

To multiply any number by 25, convert it to the nearest base i.e., 100 by multiplying it by 4. Then divide the product by 4.

Question: Multiply 19 by 25

Answer: 19 ร— 25 = (19 ร— 25 ร— 4) / 4

ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย  = (19 ร— 100) / 4

ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย  = 1900 / 4

ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย  = 475

Also Check – 20 Mental Math Shortcuts to Solve Complex Calculations in Seconds

  1. Multiplication by Application of Vedic Sutra

Step 1: LHP = (Tens digit) ร— (Tens digit + 1)

Step 2: RHP = Product of units digit in both the numbers

Step 3: Write the two parts together as the answer

Question: Multiply 44 by 46

Answer: 44 ร— 46 =ย  4 ร— 5 | 4 ร— 6

ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย  = 20 | 24

ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย  = 2024

  1. Multiplication of any number with a number which consists of only 1 like 1, 11, 111,โ€ฆ

Write the given number (multiplicand) as many times as there are 1โ€™s in the multiplier one below the other leaving the extreme left hand place unfilled and add up.

Question: Multiply 69 by 111

Answer: 6 9

ย  ย  ย  ย  ย  ย  ย  ย + 6 9

ย  ย  ย  ย  ย  ย  ย  ย + 6 9

————————–

ย ย ย ย ย ย ย ย ย ย ย ย  7 6 5 9

Conclusion

As competitive exams require speed and accuracy, students can benefit a lot by applying Vedic Math tricks in their competitive exams. Vedic Math tricks make life easier by saving time and effort.

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