Vm Nikhilam — Free Vedic Maths Tutorial
Learn Vm Nikhilam in Vedic Maths with a free, beginner-friendly tutorial, examples and practice for Indian students on Syllab.in.
TL;DR: Learn Vm Nikhilam in Vedic Maths with a free, beginner-friendly tutorial, examples and practice for Indian students on Syllab.in.
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Vm Nikhilam in Vedic Maths
Nikhilam ("all from 9 and the last from 10") is powerful for numbers close to powers of 10. For 98 × 97, both are close to 100. Deviations: 98 is 2 below 100, and 97 is 3 below. The formula is: (base − dev₁) × (base − dev₂) = base² − base(dev₁ + dev₂) + dev₁ × dev₂. Here: 100² − 100(2+3) + 2×3 = 10000 − 500 + 6 = 9506.
The method: find the base (usually the nearest power of 10), compute deviations, multiply using the formula. The genius is that the "cross product" (dev₁ × dev₂) is small and easy to compute mentally, and the middle term (base × sum of deviations) is just appending digits to the base.
This extends to any base: 28 × 32 (base 30): deviations −2 and +2. Result: 30² − 30(−2+2) + (−2)(+2) = 900 − 0 − 4 = 896. The method shines when both numbers are equidistant from the base.
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