Squaring the numbers - Shortcuts

Squaring 11_n:

If there are two digits then,
Step-1: we write the first two natural numbers (i.e., 1 and 2)
Step-2:then we write reverse

Example 11²= 12  (step-1,we write the first two natural numbers)
                  = 121 (step-2,then we write reverse)

If there are three digits then we write first three natural numbers and then we write reverse.

Example 111² = 123     (step-1,we write the first three natural numbers)
                     = 12321 (step-2,then we write reverse)

If there are four digits then we write first four natural numbers and then we write reverse.

1111²= 1234 321

Squaring a number with unit digit as 5:

Let’s say the number is R5

Now, the trick is R5² = R (R+1)/25

(here, the sign '/' does not mean division, instead it means that we have to always write 25 on the right hand side of the answer)

25² = 2 (2+1)/25
      = 625

35² = 3 (3+1)/25
     = 1225

115² = 11 (11+1)/25
       = 11*12/25
       = 13225

Squaring a number nearer to 10ⁿ:

Let’s say you have to find the value of 96²

First, find how far is 96 from 100. It is 4 digits far.

Now, write it as

96² = (96+4) (96-4) + 4²

= 100*92 + 16

= 9200 + 16

= 9216

If you practice this squaring trick well, the whole calculation can be done mentally, without using a pen.

Let’s take few more examples……………………

102² = (102 + 2) (102– 2) + 2²

       = 104 * 100 + 4

      = 10404

995² = (995 + 5) (995– 5) + 5²

        = 1000 * 990 +25

        = 990000 + 25

        = 990025

1008² = (1008 + 8) (1008 - 8) + 8²

          = 1016 * 1000 + 64

         = 1016064

Universal rule of squaring any number:

(ab)²  = a² / 2ab/b²

34² = 3² / 2*3*4/4²

      = 9/24/16

      = 1156