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Moo · #3 April 18th, 2008, 02:07 PM

Well, this goes too for 12x15 for example, which involves smaller numbers

I only gave an example with random numbers... Sometimes, there are easier ways of calculating

When I'm talking about mental calculations, I consider it as being without any paper & pen... Unfortunately, (20-1)(20-3) for some people needs some writing :-)

Another thing :

The square of a number whose unit digit is 5.

If you're looking for the square of a number N=X5 (with X representating all the digits of the number, meaning that actually, $N=10X+5$ ), don't worry, this can be shortened ^^

First of all, calculate $X(X+1)=Y$

$N^2$ will simply be $Y25 \ (100Y+25)$

For example :

$35^2 = ?$

$X=3$
$X(X+1)=3 \times 4={\color{red}12}$

Hence $35^2={\color{red}12}25$

Another example :

$115^2= ?$

$X=11$
$X(X+1)=11 \times 12={\color{red}132}$

Hence $115^2={\color{red}132}25$