SQUARING TRICK -: 3rd

Note -: when we want to square any number then we also apply another method which is as follows :
 Take an example -: 116^2 ?

Step (1).  Multiply unit digit of the given number with 2 . (6×2 = 12)

Step (2). Now multiply the given number with the number which is two times of unit digit. (116×12)

Step (3). Find the square of unit digit of the given number. (6^2 = 36 = 6×6)

Step (4). Now subtract the square of unit digit from the number which comes in step second . {( 116×12 )- 36} = 1356.

Step (5). Square the number which is  multiple of 10 comes before the given number . if 116 is given then the multiple of 10 before it is 110. (110^2 = 12100)

Step (6). Now add the numbers which we find in step '4' and step '5' , which is the answer of square of the given number .
(1356+12100 = 13456).

So , 116^2 = 13456 will be the answer..

Question(1) -: 118^2 ?

Answer -:
step(a) . unit digit is 8 in this question so ,multiply  it with two  -: 8 × 2  = 16

Step(b) . multiply the double (the answer which comes in step a) of unit digit with the
 given number -: 118 × 16= 1888

Step(c) . square the unit digit of the given number  which is 8 -: 8^2 = 64

Step(d) . now subtract the answer of step c (64) from step b (1888) -: 1888 - 64 = 1824 .

Step(e) . square the number which is multiple of 10 which comes before the given  number. 110 is the number which is multiple of 10 and come before 118 -: 110^2 = 12100.

Step( f). Now add the resultant numbers of step 'd' (1824) and 'e'(12100) -:
1824 + 12100 = 13924 .

Question -: 239 ^ 2 ?

Answer -: step (a) -: 9×2 = 18.
Step (b). 239 ×18 = 4302
Step (c). 9^2 = 81
Step (d). 4302 - 81 = 4221.
Step(e .  230^2 = 52900
Step ( f) . 52900 + 4221 = 57121
Answer willbe 57121.

Question -: 523×523(523^2) ?
Answer -: step(a). 3×2 = 6
Step(b). 523×6 = 3138
Step(c). 3×3 (3^2) = 9
Step(d). 3138 - 9 = 3129
Step(e). 520^2 = 270400
Step(f). 270400 + 3129 = 273529
Hence ans will be 273529.

Question -: 2782 ^ 2 ?
Answer -: step(a).2×2 = 4 (here unit digit number is 2 which is multiply with 2)
Step(b). 2782×4 = 11128
Step(c). 2^2 = 4
Step(d). 11128 - 4 = 11124
Step(e).2780^2 = 7728400
Step(f). 7728400 + 11124 = 7739524
Answer will be 7739524.