Squaring Trick -: 5
The square of , one (1^2 = 1 ), 11^2 = 121
In this blog we will discuss about the trick used in squaring of 1 , 11,111,11111 etc.

Squares of various number are -:
1^2 = 1
11^2 = 121
111^2 = 12321
1111^2 = 1234321
11111^2 = 123454321
111111^2 = 12345654321
111111111^ 2 = 12345678987654321
Procedure -: To find the square of number like 11,111,11111 e.t.c we apply following step

Step(1). First of all saw how many times
One (1) repeat in the number like
(a). 11 -:  in 11 , one repeat two times
(b). 111111-: in 111111, one repeat 6 times.

Step(2).let 'N' times one repeat in the given number i.e. the the number whose square is to be find  , write down successors from one to  'N'. like
(a). 1111^2 ?
And -: N = 4
Then  successors= 1234

Step(3). Now write predecessors from
'(N - 1)' to one . Like
Since N = 4
N - 1 -: 4 - 1 = 3
Now predecessors  from 3 to 1 -: 321

Step(4). Now write down the number which comes in step 3rd after the number comes in step 2nd , this number is the square of the given number.like

1111^2 = 1234321 will be the answer.

Example (2). -: 1111111^2 ?
Answer-: step(1). As we saw the given number , one comes seven time.
Step(2). Now , N = 7 , then successors from 7 to 1
Then successors = 1234567

Step(3).( N - 1 )= 7 - 1 = 6 .
Predecessor's from 6 to 1 = 654321.

Step(4). 1111111^2 = 1234567654321 will be the answer.

Note -: Similarly we find the square of any number in some second.

                       Squaring Trick -: 4


11^2 = 121   , 101^2 = 10201
In this blog we discuss squaring  tricks  for two types of number
(1). The number whose multiplication of  first digit and last digit  with 2 have a single digit .

Example -:  (a) take a number 13
If we multiply the first digit and last digit with 2 (1×3×2 = 6) then it is single digit .

(b). 12 , if we multiply first & last  digit with 2 (1×2×2 = 4) then we will get single digit

(2). The number whose multiplication of first digit & second digit with 2 have more than single digit.

Example -: (1). Let take a number 18 , if we multiply its first & second digit with 2 ( 1×8× = 16 ) which have more than one digit.

Let us start -: (1) if 11^2 = 121 , then
(a). 101^2 = 10201.
(b). 1001^2 = 1002001
(C). 100001^2 = 10000200001 and so on
What did we apply tricks  in these question?

Answer -:  step(1). In these if we palace zero between the digit of number 11,then these numbers like 101, 1001, 100001 create.
Step(2). If we want the value of 101^2 ?
Then place one zero (because if we palace one zero between the digit of 11 it will create)  between the digits of square of 11.

Like
Questions (1). 11^2 = 121 then
101^2 = 10201.
Similarly -
1001^2 = 1002001.
1000^2 = 100020001.

Question (2). (A).10002^2 ?
Answer -: step (a) 12^2 = 144
Step(b). 10002^2 = 100040004 will be the answer.
Similarly -
(B). 102^2 = 10404 and so on.

Question(3). (A). 10003^2 ?
Answer -: step (1). 13^2 = 169
Step(2). 10003^2 = 100060009.

(B). 103 ^ 2 = 10609 will be the answer.
Question (4). 201^2 ?
Answer -: step(1). 21^2 = 441
Step(2).201^2 =  40401 will be the answer.
Similarly -
2001^2 = 4004001
200001^2 = 40000400001 and so on.

Question (4). 31^ 2 = 961 then (30001)^2 = 900060001 and so on .
Similarly you find the value of
(1). 100002^2 ?
(2). 2000002^2 ?
(3). 4001^2?

Type (2).
Question (1) . (A). 2008^2 ?
Answer -: Step (a). Square the first digit, 2^2 = 4
Step (2). Multiply first & second digit with 2
-: {2×8}×2 = 32
Step (3). Square the last  digit ,8^2 = 64
Step(3). Now collect these numbers from step a to c & place one zero between every step to before collection i.e. 4032064.
Hence 2008^2 = 4032064 will be the right answer.
Note -: we put (n - 1) zero before collecting the numbers. Where ''n' is the number of zero in the given number.

Similarly
Question (2). 20008^2 = 400320064.

Question(3)200008^2 = 40003200064. And so on.
Question (4) -: 40008^2 = 1600640064

Question (5). 600008^2 = 360009600064.

Note -: If we practice these two tricks carefully then we solve these types of questions within a minute.