2 • Special case in number's square

Mental Calculation, Mathematics, and Puzzles
1

When in two numbers 0 is present.
Example - 807^2
For doing this mentally ,
First part - square first no
Middle part - multiply first and last digit and
double it
Last part - square last no.
Ans-. 64 | 8 * 7 * 2 | 49
64 | 112 | 49
651249 (middle and last part contain 2 digits because after digit 0 two digit is present and 0 itself)

Example - 906^2 = 81 | 108 | 36 = 820836

1 Like
2

In what sense if this a shortcut, when compared to the normal method for 3-digit or 4-digit squares?

(a+b)^2=a^2+2ab+b^2

Call it duplex method or call it binomial formula, but really what you’re looking at it this with your example of 807^2:

\begin{array}{rr|ll} &a &b &\\ \hline &{\color{gray}{0}}8 &07 \end{array}

I don’t understand what this has to do with “0 is present”… take 1812^2:

\begin{array}{rr|ll} &a &b &\\ \hline &18 &12 \\ \end{array}
  • before carry
\begin{array}{rr|r|r} &a^2 &2ab &b^2 \\ \hline &324 &{\color{red}{4}}32 &{\color{red}{1}}44 \end{array}
  • after carry
\begin{array}{rr|r|r} &{\color{red}{4}} &{\color{red}{1}} & \\ \hdashline &324 &32 &44 \\ \hline &\color{blue}{328} &\color{blue}{33} &\color{blue}{44} \\ \hline \end{array}
  • 1812^2=3\,283\,344

The only thing that your 0 does is that you don’t have the carry from the rightmost result, because at most you can get 09^2=81. Is that a shortcut?

3 Likes
3

@bjoern.gumboldt
With my approach you can do any type of questions which contain 0 between them

Example - 26018^2
676 | 26 * 18 * 2 | 324
676936324

Example - 5400072^2
2916 | 54722 | 5184
2916 | 7776 | 5184
29160777605184
I can do it with less than 30 seconds.

From Duplex method that is called in my country is Dwandwayog Method
Working step is more than 12 steps .
In more than 5 & 6 digits squaring.

1 Like
4

wow this method really works (: o):

26118^2

26^2 | 26 x 118 x 2 | 118^2

676 | 6136 | 13924

anything bigger than 3 digit you move forward to the next “tenth”

therefore : 676 + 6 | 136 + 13 | 924

= 682 | 149 | 924 =682,149,924 = correct according to academic math
so cool, thank you so much for sharing :DDDDDD

6

uhh I am pretty sure you can do this to all numbers with or without zeros if you see @bjoern.gumboldt 's beautifully made explaination.

8

wow this is awsome!!! I am also into math, but more to the theoretical side, such as reimann zeta function ( how if it is true - I am sure it is XD, the product of all natural numbers or prime numbers will be a finite answer) which I am focusing right now, imagine cracking the prime number code, and make everyone pay for a new online security XDDDDD

9

oh i see, that is why you prefer to use this technique when there is a 0 in the middle, what a strategy, hats off to you.

10

omg ! imagine applying the memory technique for 3 digit multiplications to see the answer immediately! life is amazing right now XD

12

ohh and you can use this technic for all x^n then you just have to know the binomial expansion of (a+b)^n which can be easily done with pascal’s triangle rule :smiley:

14

feel free to share, pretty please :smiley:

15

I am well familiar with its name in Hindi; however, this is the English speaking section of the forum. If I post in Non-English Forums I’ll make sure to translate it. Duplex is also the name Bharati Krishna Tirtha called it in English.

That is not true. You can of course use double-digits instead of single-digits in duplex, which is exactly what I have done in my above example.

Don’t worry, you’ll get faster with practice.

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