# Thread: A fast little trick for mental calculation of x^2

1. ## 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:
$\displaystyle 13^2 = 169$
Think:
$\displaystyle 1^2 = 1$
$\displaystyle 3+3 = 6$
$\displaystyle 3^2 = 9$
Excellent, should take a normally gifted person about $\displaystyle \phi$ 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:
$\displaystyle 17^2 = 289$
Think:
$\displaystyle 1^2 = 1$
$\displaystyle 7+7 = 14$
$\displaystyle 7^2 = 49$
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:
$\displaystyle f(x) = x^2 \Leftrightarrow 100\alpha^2 + 20\beta + \beta^2, x \epsilon [10, 19]$
Where alpha denotes the first digit of the product, and beta the second.

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

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

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

Have some fun!

Bye

3. 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:

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

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