Squares of Numbers with Repeated Single Digits - Tricks

1. Square of the number whose all digits are 1.
First let us check that how many times 1 is appeared, suppose 1 is appeared n times, so now start to write 1 to n in increasing order and then from n write in the decreasing order upto 1.
General Formula-
(111111……..upto n)^2 =12345…………..n………………..54321

Examples-
•             (1)^2 = 1
•             (11)^2 = 121
•             (111)^2 = 12321
•             (1111)^2 =1234321
•             (11111)^2 =123454321
•             (111111)^2 =12345654321
•             (1111111)^2 =1234567654321
•             (11111111)^2 =123456787654321
•             (111111111)^2 =12345678987654321
2. Square of the number whose all digits are 3.
First let us check that how many times 3 is appeared, suppose 3 is appeared 3 times, so now start to write (3-1=2) times 1 and then 0 and then (3-1=2) times 8 and then 9  i.e. (333)^2 =110889.
More Examples-
•             (3)^2 = 9
•             (33)^2 =1089
•             (333)^2 =110889
•             (3333)^2 =11108889
•             (33333)^2 =1111088889
•             (333333)^2 =111110888889
•             (3333333)^2 =11111108888889
•             (33333333)^2 =1111111088888889
3. Square of the number whose all digits are 9.
First let us check that how many times 9 is appeared, suppose 4 is appeared 5 times, so now start to write (5-1=4) times 9 and then 8 and then (5-1=4) times 0 and then 1  i.e. (99999)^2 =9999800001.
More Examples-
•             (9)^2 = 81
•             (99)^2 =9801
•             (999)^2 =998001
•             (9999)^2 =99980001
•             (99999)^2 =9999800001
•             (999999)^2 =999998000001
•             (9999999)^2 =99999980000001
•             (99999999)^2 =9999999800000001
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