SHORTCUTS FOR SQUARING A NUMBER

 SQUARING A TWO DIGIT NUMBER:

Method1:

 

1 2 2      =	12 (1st digit) (1)	2x1x2 (2 x 1st digit  x 2nd digit) (2)	22 (2nd digit) (1)
	1	4	4
	=      1 4 4
2 9 2      =	22 (1st digit) (1)	2x2x9 (2 x 1st digit  x 2nd digit) (2)	92 (2nd digit) (1)
	4	36	81
	4 + 4  = 8	36  + 8  = 4 4	81
	=      8 4 1
8 6 2      =	82 (1st digit) (1)	2x8x6 (2 x 1st digit  x 2nd digit) (2)	62 (2nd digit) (1)
	64	96	36
	64  +  9  = 73	96  +  3  = 99	36
	=      7 3 9 6

Method2:

x	2	4
	2	4
=   5   7   6

2   2 (1st column)	2    4   2    4 (All columns)	4   4 (3rd  column)
(2x2) =4	(2x4)+(2x4) = 8+8 =16	(4x4) = 16
= 4 +1 =5	=16+1 =17	=16

SQUARING A THREE DIGIT NUMBERS:

Method1:

1 2 22      =	12   (1st digit) (1)	2x1x2   (2 x 1st x 2nd digit) (2)	(2x1x2) + 22   (2 x 1st  x 3rd digit) + (2nd digit)2  (3)	2x2x2   (2 x 2nd x 3rd digit)  (2)	22   (3rd digit) (1)
	1	4	8	8	4
	=  1 4 8 8 4
2 4 82      =	22   (1st digit) (1)	2x2x4   (2 x 1st x 2nd digit) (2)	(2x2x8) + 42   (2 x 1st  x 3rd digit) + (2nd digit)2  (3)	2x4x8   (2 x 2nd x 3rd digit)  (2)	82   (3rd digit) (1)
	4	16	48	64	64
	4 + 2  = 6	16  +  5    =  2  1	48+ 7        = 5 5	64+ 6  = 7 0	64
	=   6 1 5 0 4

 

Method2:

12  2 2      =	122 (1st two digit)2 (1)	2x12x2 (2 x 1st two digit  x 3rd digit) (2)	22 (3rd digit) (1)
	144 + 4 = 1 4 8	48	4
	=  1 4 8 8 4

 

 

 

 

 

Method3:

x	1	2	2
	1	2	2
=   1  4   8   8   4     1   1 (1st column) 1     2   1     2 (first two columns) 1     2    2   1     2    2 (all columns) 2     2   2     2 (last two columns) 2   2 (3rd column) (1x1) = 1   (1x2)+(1x2) = 2+2 =4 (1x2)+(1x2)+(2x2) = 2+2+4 =8   (2x2)+(2x2) = 4+4 =8   (2x2) =4