Squaring shortcut method

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

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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?

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@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.

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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

@Oscar4
But in this you calculated in middle part 3 digit calculation.
I have fastly do 2 digit calculation in mind
And for 3 digit calculation I am just slow

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.

@Oscar4
I have made our own Method for finding different type of square of numbers

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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

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.

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

Ya, it can done by practice and logic only.

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:

I know pascal triangle and algebraic formula
But I use different approach

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feel free to share, pretty please :smiley:

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 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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