Friday, June 27, 2014

Trick to square a number.

If number is divisible by 5. This is very easy to get the square of such number.

Suppose it is a two digit number:
xy = (x* (x+1)) (y*y)

Example:
15 = 1*(1+1)    (5*5) =  (1*2) 25 =  225
25 = 2*(2+1)    (5*5) =  (2*3) 25 =  625
35 = 3*(3+1)    (5*5) =  (3*4) 25 = 4225
45 = 4*(4+1)    (5*5) =  (4*5) 25 = 2025
125 = 12*13     (5*5) = 15625

Trick to get the Square of other numbers that are below than hundred
xy =   x*(xy+y)+Carry + (y*y)

Example
12 = (1*(12+2) +0) (2*2) =( (1*14)+0)  4 = 144
13 = (13+3) (3*3) = 169
14 = (14+4) (16)  = 196 (Carry will be 1 that will add in 18)
15 = (15+5) (25) = 225
21 = 2*(21+1) (1)= 441
22 = 2*(22+2) (2*2) = 484
26 = 2*(26+6) (6*6) =  676
32 = 3*(32+2) (2*2) =  1024

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