Introducing our new series on Vedic Mathematics: “Unveiling the 16 Sutras”. An ancient system of mathematics that originated in ancient India, Vedic Mathematics provides various techniques and sutras (formulas) to perform calculations quickly and efficiently.
Recommended Reading: Vedic Math Sutras: Sutra 2-Nikhilam Navatashcaramam Dashatah
In this educational journey, we embark upon unraveling the ancient techniques, and we are beginning with the powerful sutra called Ekadhikena Purvena, a shortcut to square.
Translated as “by one more than the previous,” this sutra is the foundation for mental calculations and is the key to unlocking mathematical prowess.
This versatile technique simplifies multiplication when the unit digit sum of two numbers is 10.
Steps
Here is the step-by-step process of applying the Ekadhikena Purvena sutra:
“Ekadhikena Purvena” is a sutra (formula) in Vedic mathematics, which means “By one more than the previous one.” This sutra is used to square numbers close to a power of 10, typically when the number’s last digit(s) is(are) small.
But 45 is far from a power of 10. If we apply the sutra directly, the calculations are pretty complicated.
However, if you still want to use the Ekadhikena Purvena method, you can use the nearest base of 50, which is more convenient.
Let’s apply the Ekadhikena Purvena sutra to find the square of 45.
1. First, split the number into two parts: the part that doesn’t include the 5 (4 in this case) and the 5.
A: 4
B: 5
2. Now, take the part of the number that doesn’t include the 5 (4) and add 1, making it 5.
C: 4+1=5
3. Multiply the original number that doesn’t include the 5 (4) by the number you just calculated (5). This gives you 20.
AXC
4×5= 20
4. Then append 25 (the square of 5) to the result from step 3.
So, the result is 2025
The next one will be Nikhilam Navatashcaraman Dashatah.
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