How to find the square of any Number

 

If we know how to find the square of any number, then you can find any number’s square in just one or half minutes. It will be very easy to us to find out he square of any number.

If we want to find the square of any number follow this formula a²= (a + b)*(a - b) + b². In this formula: -

        a²   = the number’s square we want to find.

  (a + b)= in this ‘a’ is the original number and ‘b’ is the number at ones place.

 

Steps: -

If we want to find the square of 67 then: -

  a²=(a + b)*(a – b) + b²

  Therefore:-

1.   67²= (67 + 7)*(67 - 7) + 3²

2.   67²= 74 * 60 + 9

3.   67²= 70 * 60 + 4 * 70 + 9

4.   67²= 4200 + 280 + 9

5.   67²= 4489

 

Thus, 4489 is the square of 67. Very easy na!

 

Examples: -

(Q) Find the square of 108

  a²=(a + b)*(a – b) + b²

  Therefore:-

1.   108²= (108 + 8)*(108 - 8) + 8²

2.   108²= 116 * 100 + 64

3.   108²= 11600 + 64

4.   108²= 11664

 

 

(Q) Find the square of 998

  a²=(a + b)*(a – b) + b²

  Therefore:-

    1. 998²= (998 + 8)*(998 - 8) + 8²

    2. 998²= 1006 * 990 + 64

    3. 998²= (1000 * 990) + (6 * 990) + 64

    4. 998²= 990000 + 5940 + 64

    5. 998²= 996004

 

 

(Q) Find the square of 65

  a²=(a + b)*(a – b) + b²

  Therefore:-

    1. 65²= (65 + 5)*(65 - 5) + 5²

    2. 65²= 70 * 60 + 25

    3. 65²= 4200 + 25

    4. 65²= 4225

 

 

(Q) Find the square of 89

  a²=(a + b)*(a – b) + b²

  Therefore:-

    1. 89²= (89 + 9)*(89 - 9) + 1²

    2. 89²= 98 * 80 + 1

    3. 89²= (90 * 80) + (8 * 90) + 1

    4. 89²= 7200 + 720 + 1

    5. 89²= 7921

 

(Q) Find the square of 37

  a²=(a + b)*(a – b) + b²

  Therefore:-

    1. 37²= (37 + 7)*(37 - 7) + 3²

    2. 37²= 44 * 30 + 9

    3. 37²= (40 * 30) + (4 * 40) + 9

    4. 37²= 1200 + 160 + 9

    5. 37²= 1369