Squaring Any Number Using Duplex Method
H.D. Motiramani
Squaring becomes very easy by using this method using duplex of numbers. Let us first know what duplex of different digits is calculated. Let us say single digit is ‘a’, two digits are ‘ab’, three digits are ‘abc’, four digits are ‘abcd’ and so on.
Duplex of ‘a’ = a²
Duplex of ‘ab’ = 2ab
Duplex of ‘abc’ = 2ac + b²
Duplex of ‘abcd’ = 2ad + 2bc
Duplex of abcde = 2ae +2bd + c²
Examples:
(ab)² = duplex of a I duplex of ab I duplex of b = a² I 2×a×b I b²
(76)² = duplex of 7 I duplex of 76 I duplex of 6 = 7² I 2×7×6 I 6² = 49 I 84 I 36 = 5776
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(abc) ² = Duplex of a I Duplex of
ab I Duplex of
abc I Duplex of
bc I Duplex of c
(723) ² = 7² I 2×7×2 I 2² +2×7×3 I 2×2×3 I 3²
= 49 I 28 I 46 I 12 I 9
= 522729
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(abcd) ² = duplex of a I duplex of
ab I duplex of
abc I duplex of abcd
I Duplex of bcd I duplex of
cd I
duplex of d
(5432) ² = 5² I 2×5×4 I 4² + 2×5×3 I 2×5×2 + 2×4×3 I 3² + 2×4×2 I 2×3× 2 I 2²
= 25 I 40 I 46 I 44 I 25 I 12 I 4
= 29506624
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