Question

Find the square of the following numbers by Dvanda yoga method or Duplex process:

(a) 53214

(b) 31321

Answer 1

(a) 53214²

= Dvanda of 5 / Dvanda of 53 / Dvanda of 532 / Dvanda of 5321 / Dvanda of 53214 / Dvanda of 3214 / Dvanda of 214 / Dvanda of 14 / Dvanda of 4

= 5² / 2 x 5 x 3 / 2 x (2 x 5) + 3² / 2 x (5 x 1) + 2 (3 x 2) / 2 (5 x 4) + 2 (3 x 1) + 2² / 2 (3 x 4) + 2 (2 x 1) / 2 x (2 x 4) + 1² / 2 x 1 x 4 / 4²

= 25 / 30 / 29 / 22 / 50 / 28 / 17 / 8 / 16

= 2831729796

(b) 31321²

= Dvanda of 3 / Dvanda of 13 / Dvanda of 132 / Dvanda of 3132 / Dvanda of 31321 / Dvanda of 1321 / Dvanda of 321 / Dvanda of 21 / Dvanda of 1

= 3² / 2 x 1 x 3 / 2 (1 x 2) + 3² / 2 x (3 x 2) + 2 (1 x 3) / 2 (3 x 1) + 2 (1 x 2) + 3² / 2 (1 x 1) + 2 (3 x 2) / 2 x (3 x 1) + 2² / 2 x 2 x 1 / 1²

= 9/6/13/18/19/14/10/4/1

= 981005041