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.
The following steps are involved in the squaring process: Step 1: The square of the given number has two parts – 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 × (15 +1) | 52 = 240 | 25 = 24025 |
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Step 1: The square consists of three parts – 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 = 22 | 2 × 2 × 9 | 92 = 4 | 36 | 81 = 4 | 36 + 8 = 44 | 1 = 4+4 | 4 | 1 = 8 | 4 | 1 = 841 |
- 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 – 700)2
= 716 + 16 | (16)2
= 732 × 7 | 256
= 5124 + 2 | 56
= 512656
- 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 – 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: 912 = 91 – (100-91) | (100-91)2
= 91 – 9 | 92
= 8281
- 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: 1052 = 105 + (105-100) | (105-100)2
= 105 + 5 | 52
= 110 | 25
= 11025
- 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 – 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: 9832 = 983 – (1000 – 983) | (1000 – 983)2
= 983 – 17 | 172
= 966 | 289
= 966289
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- 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 × 50 = (289 × 50 × 2) / 2
= (289 × 100) 2
= 28900/2
= 14450
- 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 × 25 = (19 × 25 × 4) / 4
= (19 × 100) / 4
= 1900 / 4
= 475
- Multiplication by Application of Vedic Sutra
Step 1: LHP = (Tens digit) × (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 × 46 = 4 × 5 | 4 × 6
= 20 | 24
= 2024
- Multiplication of any number with a number which consists of only 1 like 1, 11, 111,…
Write the given number (multiplicand) as many times as there are 1’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
+ 6 9
+ 6 9
————————–
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.
