The Square of Any Two-digit Number

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In this Math Trick, we are going to square any two-digit number.

 

It is represented by, the formula,

(10X + Y)² = 100X2 + 20XY + Y2

Or by Square of Binomial Method, with HTO, HundredsTensOnes (1st2nd3rd-Digits)

Let's solve for,

1. 12², 2. 23² 3. 872

Solution:

1a. 12² = 100*1² + 20*1*2 + 22

             = 100 + 40 + 4

             = 144

1b. By Square of Binomial Method :

12² = 1² for the first digit l 1*2*2 for the second digit l 2²

        = 1 l 4 l 4

        = 144

2a. 23² = 100*2² + 20*2*3 + 32

            = 400 + 120 + 9

            = 529

2b. By Square of Binomial Method:

23² = 3² for the first digit l 2*3*2 for the second digit l 3²

       = 4 l 12 l 9

       = 529 (see my YouTube video)

3a. 87² = 100*8² + 20*8*7 + 72

            = 6400 + 1120 + 49

            = 7,520 + 49

            = 7,569

3b. By Square of Binomial Method:

87² = 8² for the first digit l 8*7*2 for the second digit l 7²

       = 64 l 112 l 49

       = 7,569 (see my YouTube video)

You may notice that I made the multiplication from left to right. It actually has a purpose.You can immediately tell what's the first digit of the answer. And if it is a 3 or 4 digit number. 

This will be the beginning of solving it orally. You'll be amazed that you can solve it orally if you just continue practicing.