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LEVEL 6
Vedic Squaring
The Vedic Base Method
Key Formula
n² = (n + d) × base + d²
where d = n - base (the deviation)
Step 1 — Pick a Base
Choose the nearest base: 10, 100, or 1000. For 103, use base 100.
Step 2 — Find Deviation
d = your number − base. For 103: d = 103 − 100 = 3. For 97: d = 97 − 100 = −3.
Step 3 — Compute Left Part
(n + d) = n + (n − base) = 2n − base. For 103: 103 + 3 = 106.
Step 4 — Compute Right Part
d² (square the deviation). For 103: 3² = 9. Write as 2-digit: 09.
Step 5 — Combine
Left part × base + right part. For 103: 106 × 100 + 9 = 10609.
Examples
103² = ?
d = 103 − 100 = 3
Left: 103 + 3 = 106
Right: 3² = 09
= 106 | 09 = 10609
97² = ?
d = 97 − 100 = -3
Left: 97 + -3 = 94
Right: -3² = 09
= 94 | 09 = 9409
12² = ?
d = 12 − 10 = 2
Left: 12 + 2 = 14
Right: 2² = 4
= 14 | 4 = 144
8² = ?
d = 8 − 10 = -2
Left: 8 + -2 = 6
Right: -2² = 4
= 6 | 4 = 64
When to Use Which Base
Numbers 7–13Use base 10
Numbers 90–110Use base 100
Numbers 900–1010Use base 1000
Negative deviation (97, 8)Still works! d is negative, d² is still positive.