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.

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 ✓

✏️ Practice

Work it out in your head or on paper, type the answer and press Check. Stuck? Press “Show me how”.

Right: 0 · Tried: 0

🏁 Trick 26 test

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

🏅 Sign in with Google to earn the 💠 Duplex Master badge when you pass — and a certificate when you finish all 10 tricks of Part 3 · Expert tricks. You can still take the test without signing in.

🖨️ Squares of 3 Digit Numbers Worksheet

✨ Free AI tutor

Ask the AI tutor about this trick

Why does it work? When should you use it? Ask in English, मराठी or हिंदी.

👩‍🏫 Vedic maths classes near you — online or at home

Prefer a real teacher? TalentJR teachers take live online classes anywhere in India and visit homes in selected cities. Tell us what you need and our team will call you with timings and fees.

Live online classesSmall groups or 1:1 with a teacher, from home, any city.

Teacher at homeA TalentJR teacher visits your home (selected cities).

At a centreClasses at a TalentJR partner centre near you, where available.

Badges, certificates & gifts A badge for every trick you pass, a certificate for every part you finish, plus TalentJR Points for daily practice. Abacus course Younger child? Start with the free abacus course (ages 5–14).