Hi friends, Here we are giving a shortcut tip to find square of a number having all digits are 1s or 3s or 9s. There is another way to find a square of a number having same digits. But this tip is take less time than other tips. Here we are explaining both shortcut tips:
Square of a Number have All the Digits Same:
2 digits | 3 digits | 4 digits | |
Number | xx | xxx | xxxx |
Answer | X^{2} | 2X^{2} | X^{2} | X^{2} |2 X^{2} | 3X^{2} | 2X^{2} | X^{2} | X^{2} | 2X^{2} | 3X^{2} | 4X^{2} | 3X^{2} | 2X^{2} | X^{2} |
Example | 88 | 666 | 3333 |
Answer | 64 | 128 | 64 | 36 | 72 | 108 | 72 | 36 | 9 | 18 | 27 | 36 | 27 | 18 | 9 |
88^{2} = ?
666^{2} = ?
2 digits (1, 2, 1)
3 digits (1, 2, 3, 2, 1)
4 digits (1, 2, 3, 4, 3, 2, 1)
5 digits (1, 2, 3, 4, 5, 4, 3, 2, 1)
6 digits (1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1)
7 digits (1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 1)
8 digits (1, 2, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3, 2, 1)
9 digits (1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1)
If All numbers are 1
Answer is 1, 2, 3 ….. to the number of 1s in the number and reverse to 1
Example: 1111111
There are 7 1s in the number
So, Answer is = 1234567654321
If All numbers are 3
If there is n 3s
Then answer is (n-1) 1s, 0 , (n-1) 8s, 9
Example: 3333^{2}
There are 4 3s then answer is 11 0 88 9 = 110889
Example 2: 333333
There are 6 3s then answer is 1111 0 8888 9 = 1111088889
If All numbers are 9
If there is n 9s
Then answer is (n-1) 9s, 8 , (n-1) 0s, 1
Example: 99999^{2}
There are 5 9s then answer is 9999 8 0000 1 = 9999800001
Example 2: 999
There are 3 9s then answer is 99 8 00 1 = 998001