Vedic maths · trick 26 of 36 · free

Squares of 3- and 4-digit numbers — Vedic maths trick

Trick 7 squared 2-digit numbers with the duplex. The duplex works for any number of digits: one digit → its square; two → twice their product; three → twice the outer pair plus the middle squared.

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The trick

Dwandwa Yoga — “the duplex”

For abc: columns D(a) | D(ab) | D(abc) | D(bc) | D(c).
D(a) = a², D(ab) = 2ab, D(abc) = 2ac + b², D(abcd) = 2ad + 2bc.
Combine from the right with carries.

Use it for: Squares of 101 to 9999.

Worked example: 123² = 15129

D(1) = 1; D(12) = 4; D(123) = 2×1×3 + 2² = 10; D(23) = 12; D(3) = 9.
From the right: 9; 12 → 2 carry 1; 10 + 1 = 11 → 1 carry 1; 4 + 1 = 5; 1.
Answer: 15129.

Check: 123 × 123 = 123 × 100 + 123 × 23 = 12300 + 2829 = 15129 ✓

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✓ Written and checked by the TalentJR team · Updated 13 Oct 2026 · How we make our lessons

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🏁 Trick 26 test

20 sums. Check each answer, then go to the next one. Get 16 or more right to pass.

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🖨️ Squares of 3 Digit Numbers Worksheet

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