12: SQUARING NUMBERS, ENDING IN 1

SUTRA (Algorithm):

Read & Work from Right
SQUARE | DOUBLE | 1

'Double' is double of the REST;
'Square' is square of the REST
& REST is the Number without '1'

Demonstration (1): 312 = ?

sq 1 ending_215x200

In 31, if you take 1, the REST is '3'.

312 = 3 x 3 | 3 + 3 | 1
312 = 9 6 1
[or]
312 = 32 | 2 x 3 | 1
312 = 9 6 1

Demonstration (2): 412 = ?

Read & Work from Right
412 = 42 | 2x4 | 1 = 1681

Demonstrations:

Read & Work from Right
  1. 812 = 82 | 2x8 | 1 = 65161
  2. 1012 = 102 | 2x10 | 1
    1012 = 102201
  3. 1512 = 225|30|1 = 228301
  4. 2512 = 625|50|1 = 630501
  5. 3212 = 1024|64|1 = 1030641
  6. 21012 = 44100|420|1
  7. 21012 = 441424201

Just write the squares mentally on the right:

  1. 212 =
  2. 712 =
  3. 1012 =
  4. 1212 =
  5. 2012 =
  6. 2112 =
  7. 1512 =
  8. 1812 =
  9. 2212 =
  10. 3512 =
  11. 5012 =
  12. 40012 =