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Squaring Numbers a New Way ............

 
 
Reply Fri 15 Apr, 2016 02:02 am
Squaring Numbers a New Way by PiyushGoel
If we talk about Square,Square is the result of multiplying a number by itself.From ancient lot creative man has given lot to Mathematics about Squaring and more yet to come into existence,one of Mathematics Lover PiyushGoel has done more in Squaring.
If we square 11,simply put 1(2*1)(1^2) get 121 same as square of 12 = 1(2*2)(2^2) get 144 and for 13&14 get receptively 169 196.
Look at (2,4,6,8,10,12 ,14,16,18,20 …diff of 2) & (1, 4 , 9 ,16,25,36,49,64,81,100 ……diff. is 3 5 7 9 11 13 15 17 19) and diff. of 3 5 7 9 11 is 2, so there is true symmetry of 2.
11^2 = 1 2 1
12^2 = 1 4 4
13^2 = 1 6 9
14^2 = 1 8 16 = 100 + 80 + 16 = 196
15^2 = 1 10 25 = 100 + 100 + 25 = 225
16^2 = 1 12 36 = 100 + 120 + 36 = 256
17^2 = 1 14 49 = 100 + 140 + 49 = 289
18^2 = 1 16 64 = 100 + 160 + 64 = 324
19^2 = 1 18 81 = 100 + 180 + 81 = 361
20^2 = 1 10^2 = 1 20 100 = 100 + 200 + 100 = 400
21^2 = 1 11^2 = 1 22 121 = 100 + 220 + 121 = 441
22^2 = 1 12^2= 1 24 144 = 100 + 240 + 144 = 484
23^2 = 1 13^2 = 1 26 169 = 100 + 260 + 169 = 529
24^2 = 1 14^2 = 1 28 196 = 100 + 280 + 196 = 576
25^2 = 1 15^2 = 1 30 225 = 100 + 300 + 225 = 625
26^2 = 1 16^2 = 1 32 256 = 100 + 320 + 256 = 676
27^2 = 1 17^2 = 1 34 289 = 100 + 34 + 289 = 729
28^2 = 1 18^2 = 1 36 324 = 100 + 360 + 324 = 784
29^2 = 1 19^2 = 1 38 361 = 100 + 380 + 361 = 841
30^2 = 1 20^2 = 1 40 400 = 100 + 400 + 400 = 900
31^2 = 1 21^2 = 1 42 (1 11)^2 = 1 42 (1 22 121)
= 961 = 121 + 220 + 100
= 441 + 420 + 100 = 961
41^2 = 1 31^2 = 1 62 (1 21)^2 = 162 (1 42) (1 11)^2
= 1 62 (1 42) (1 22 121)
= 1 62 (961) = 961 + 620 + 100 = 168
Copyrighted to PiyushGoel
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Type: Discussion • Score: 1 • Views: 1,014 • Replies: 2
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fresco
 
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Reply Sat 16 Apr, 2016 01:51 am
@PiyushGoel,
Smile Forget the copyright rubbish !
Learn a bit of elementary algebra to understand that your 'method' is a convoluted restatement of the identity
(a+b)^2 = a^2+2ab+b^2
e.g.
41^2 = (40+1)^2 = 40^2 + 2*40*1 + 1^2 =1600 + 80 + 1 = 1681
alternatively, you can make it more complicated LIKE YOU by writng
41 as a different combination, such as 30+11 etc !
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fresco
 
  1  
Reply Sat 16 Apr, 2016 02:20 am
@PiyushGoel,
...or 10+31, giving 10^2+2*10*31+31^2=100+620+900+60+1
....YOUR GROUPING !
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