SQUARE OF REPETED NUMBERS

SQUARE OF REPEATED   NUMBERS

1’S

(1)²                                                 =                     1

(11)²                                               =                   121

(111)²                                             =                 12321

(1111)²                                           =               1234321

(11111)²                                         =             123454321

(111111)²                                       =           12345654321

(1111111)²                                     =         1234567654321

(11111111)²                                   =       123456787654321

3’S

(3)²                                                 =                     9

(33)²                                               =                   1089

(333)²                                             =                 110889

(3333)²                                           =                11108889

(33333)²                                         =             1111088889

(333333)²                                       =           111110888889

6’S

(6)²                                                 =                     36

(66)²                                               =                   4356

(666)²                                             =                 443556

(6666)²                                           =                44435556

(66666)²                                         =             4444355556

(666666)²                                       =           444443555556

9’S

(9)²                                                 =                     81

(99)²                                               =                   9801

(999)²                                             =                 998001

(9999)²                                           =                99980001

(99999)²                                         =             9999800001

(999999)²                                       =           999998000001

UNIVERSAL METHOD TO FIND SQUARE OF ANY NUMBER

UNIVERSAL METHOD TO FIND SQUARE OF ANY NUMBER:

METHOD 1:

1.   1.  a²/2ab/b²

Example: 

Que 1  :  Find  (46)²

Soln: 
            Here a= 4

               &   b=6

(46)² = 4² / 2 X 4 X 6 / 6²

        = 16 / 48  /36

   

   //   16+4 + carry(1) / 1 / 6

         =2116 ans.

 Example:

Que2 :  Find  (116)²

Soln: 
            Here a= 11

               &   b=6

(116)²     = 11² / 2 X 11 X 6 / 6²

            = 121 / 132 / 36

 

   //   121+13  / 5 / 6

         =13456 ans.

Example:

Que3 :  Find  (22)²

Soln: 
            Here a= 2

               &   b=2

(22)² = 2²/ 2 X 2 X2 /2²

        = 4/8/4

        = 484 ans.

Example:

Que3 :  Find  (10002)²

Soln: 
            Here a= 1000

               &   b=2

(10002)² = 1000² / 2 X 1000 X2 / 2²

        = 1000000 / 4000 / 4

        = 100040004  ans

METHOD 2:

1.      (a + b)² = a² + 2ab + b²

Example:

Que1 :  Find  (25)²

Soln: 

         25 = 20 + 5
                     Here a= 20

                    &   b=5

         (25)²   = 20² + 2 X 20 X 5 + 5²

                    = 400 + 200 + 25

                    = 625  ans.

Example:

Que2 :       Find  (1003)²

Soln:        1003  =  1000 + 3
                 Here a= 1000

                 &   b=3

(1003)²     = 1000² + 2 X 1000 X 3 + 3²

                 = 1000000 + 6000 + 9

                 = 1006009   ans

2.      (a - b)² = a²  - 2ab + b²

Example:

Que1 :  Find  (19)²

Soln: 

     19 = 20 - 1
                 Here a= 20

                  &   b=1

       (19)² = 20² + 2 X 20 X 1 + 1²

               = 400 - 40 + 1

               = 361  ans.

Example:

Que2 :         Find  (97)²

Soln:          97  =  100 - 3
                  Here a= 100

                  &   b=3

          (97)² = 100² - 2 X 100 X 3 + 3²

                   = 10000 – 600 + 9

 = 9409   ans

TO FIND SQUARE OF ANY NUMBER.

HELLO!!! Frndzzz…
 HERE ARE SOME IMPORTANT TRICKS TO LEARN...

TO FIND SQUARE OF ANY NO.

METHOD  1:

WHEN THE LAST DIGIT IS "5"

EXAMPLE:
Que 1 .    FIND (25)²
Soln:    (2 X 3) 25   // multiply the first digit to its next digit and write 25 at last

       // next number to 2 is 3 so <3x2=6>

            =625 ans.


Que 2:    Find (75)²
Soln:     (7X8)25
            = 5625 ans

Que 3 :  Find (105)²
Soln:    (10X11)25
            =11025 ans. 

METHOD  2:

WHEN THE NUMBER IS BETWEEN 40 to 60

 Steps to find the square between 40-60 :

Note : Remember 25 in these number .. its your friend now and it will help you to find solution.
Here  may be two conditions:

1.      When the number is greater than 50

example:

Que 1. Find  (54)²

soln:  1. Add last digit into 25 (25+4 = 29)

         2.  find the square of last digit (here last digit is 4  so 4² =16)

         3. The ans is Step 1 + step 2

        4.  2916  is your ans.

Que 2.  Find (57)²

Soln:  (25+7)7²

          = 3249 ans.

Que 3: find   (59)²

Soln :  (25+9)9²

          = 3481 ans.


FIND : (69)²
Soln:  69= 50+19
       (69)²=(25+19)19²
               = (44+carry3)61

               = 4761 ans.

3.When the number is less  than 50

 example:

Que 1.  Find  (44)²

Soln :  1. Find the difference of the number to 50 < here 50 - 44 = 6  >

         2.  Subtract  last difference  from 25 (25-6 = 19)

         3. find the square of difference  digit (here last digit is 6  so 6² =36)

        4.  The ans is Step 2 + step 3

        5. 1936 is your ans.

Que 2.  Find  (34)²

Soln:  34= 50-16
       (34)²=(25-16)16²
               = (9+carry 2 )56

               = 1156 ans.

METHOD  3:

WHEN THE NUMBER IS GREATE THAN 100

example:

Que 1. Find  (102)²

Soln:  By Vedic method:

            102X102

            100      02                

            100      02

--------------------------------

            A         B

 

                 

100      02                

            100      02

________________________

            104      04  = 10404 ans.

Example 2 :

Que 1. Find  (108)²

Soln:  By Vedic method:

            108X108

=          100      08                

            100      08

_____________________

100+08+08     08X08

=          100      08                

            100      08

______________________

            116      64  =  11664 ans.

METHOD 4:

WHEN THE NUMBER IS LESS THAN 100

Example:

Que 1. Find  (92)²

Soln:  By Vedic method:

            92X92

            100      -08                

            100      -08

--------------------------------

            A         B

100      -08                

            100      -08

________________________

100-08-08        64   =  8464 ans.

Example  :

Que 2. Find  (94)²

Soln:  By Vedic method:

108X108

=          100      -06                

            100      -06

_____________________

100-06-06     -06X-06   = 8836 ans.

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