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.