A fast little trick for mental calculation of x^2

• Jan 26th 2006, 11:09 AM
dud
A fast little trick for mental calculation of x^2
I suppose many might have figured this out, but it's a neat little mind trick for calculating the product of a number between 10 - 19 with itself. I stumbled upon it as I was riding the bus back home from my math class, and thought it might come in handy for those who don't know it yet!

Multiplication:
$
13^2 = 169
$

Think:
$
1^2 = 1
$

$
3+3 = 6
$

$
3^2 = 9
$

Excellent, should take a normally gifted person about $\phi$ seconds! ;)

For numbers which gives two digits for any of the operations, you do the same basically. But just remember that you need to summarize the results you get correctly.
Multiplication:
$
17^2 = 289
$

Think:
$
1^2 = 1
$

$
7+7 = 14
$

$
7^2 = 49
$

If you remember the addition you need to do, it shouldn't take much longer.

This metod works excellently for myself, and it will usually take me between 2-5 seconds to calculate the product of any number between 10-19 multiplicated with itself.

A bit more mathematically we can write:
$
f(x) = x^2 \Leftrightarrow 100\alpha^2 + 20\beta + \beta^2, x \epsilon [10, 19]
$

Where alpha denotes the first digit of the product, and beta the second.
• Jan 26th 2006, 11:33 AM
earboth
Quote:

Originally Posted by dud
I suppose many might have figured this out, but it's a neat little trick...

Hey,

$37 \cdot 43 = 1600 - 9$
or $79 \cdot 81 = 6400 - 1$

For heaven's sake, why that? Can you explain how it works?

Have some fun!

Bye
• Jan 26th 2006, 11:58 AM
earboth
Quote:

Originally Posted by dud
I suppose many might have figured this out, but it's a neat little trick...

Hey,

here I'm again. The following way to calculate a product of two numbers is really tricky to explain - but try it:

$\begin{array}{l cr} 37 \cdot &42\\ 18 & 84\\9 & 168\\4&336\\2&672\\1&1344\end{array}$

You've to delete now all numbers of the second column corresponding to an even number in the first column.
That leaves yo with: 42+168+1344

and the result of this sum is 1554 = 37 * 42

Now it's your turn.

Have much fun!

Bye
• Jan 26th 2006, 12:02 PM
dud
That last one is neat, but it might happen to be a little too much to keep in your head at one time! :p Especially if you're attention is diverted for a bit.
Also I recon it would take a few minutes of effort for most numbers, right?

But a good little thing indeed.
Mine is cooler though! :D
Has anyone used/seen this one before by the way?