Vedic Math-2 Squares

Vedic Math – Squares of Numbers

How to Find Squares of Single Digit or 2 Digit Numbers.

82 = (10-2)2 = 100 – 40 + 4 = 10(10-4) + 4
= 10(10-2-2) + 22 = 10(8-2) + 22 = (8-2)/22 = 64

92  =  (9-1)/12 = 8/1 = 81
Here 9 is 1 less than 10(Base 10), So deficiency =1
Reduce it still further to that extent, So (9-1) = 8.
Square its deficiency, So 12 = 1 .
Final Answer: 81

132 = (13+3)/32 = 16/9  = 169
Here 13 is 3 more than 10(Base 10), So Excess = 3
Increase it still further to that extent, So (13+3) = 16
Square its excessive, So 32= 9
Final Answer: 169

182 = (18+8)/82 = 26/64 = 32/4 = 324
Here 18 is 8 more than 10(Base 10), so Excess = 8
Increase it still further to that extent, So (18+8) = 26
Square its excessive, So 82= 64. As we are using Base 10, 6 gets carry forwarded to other side.
Final Answer: 324  {Where First term at tens place and last term at Units place}

It is a specific and shortcut to square numbers is closer to power of 10. (10, 100, 1000, ….)

Square of 14:

142 = (14+4)/42 = 18/16  = 196

Here 14 is 4 more than 10(Base 10), So Excess = 4
Increase it still further to that extent, So (14+4) = 18
Square its excessive, So 42= 16
Final Answer: 196

Square of 97:

972 = (97-3)/32 = 94/09  = 9409

Here 97 is 3 less than 100(Base 100), So deficiency =3
Reduce it still further to that extent, So (97-3) = 94.
Square its deficiency, So 32 = 09. (As base is 100, we need exactly 2 digits. Hence 09).
Final Answer: 9409

Practice :

  • 932= (93-7)/72 = 86/49 = 8649
  • 892= (89-11)/112 = 78/121 = 7921
  • 1132 = (113+13)/132 = 126/169 = 12769
  • 10022 = (1002+2)/22 = 1004/004 = 1004004