My Mathematical Theories

HOW To Recite Perfect squares Without Memorizing?-Part 1

0²=0

1²=1

2²=4

3²=9

4 ²=16

5²=25

6²=36

7²=49

8²=64

9²=81

10²=100

11²=121

12²=144

13²=169

14²= 196

15²= 225 

Observe the pattern,the las digits of perfect squares are 0,1,4,9,6,5,6,9,4,1,0 and back again to 1-0.Therefore,we have now a one digit clue in reciting perfect squares.

And for our Remaining digits the pattern is...

For first 3,0 is excluded,n² the first digit is 0

the 4²,5²,6²,7² have 1 adjacent difference on their 1st digit

49,36,25,16

4-3=1

3-2=1

2-1=1

It means every remaining digits are will be added to 1

BUT the excemption is the pattern will change in every n that the last digit is 3 and 7.

1²=01 the first pattern is to add 0 in every remaining digits[n/a:the 0 on first digit just only a guide]Just follow the pattern on every last digits.(1,4,9,6,5,6,9,4,1,0...)

2²=04

3²=09 the n is 3.Therefore,the pattern will change by adding 1 on the remaining digits

4²=16 

5²=25

6²=36

7²=49 The n is 7.Therefore,the pattern will change by adding 2 on the remaining digits

8²=64

9²=81

10²=100 Explain.8+2=10

11²=121

12²=144

13²=169

And so on.

BLANK