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Moo · #9 April 20th, 2008, 05:49 AM

Check for the unit digits (and cubic roots of numbers)

In general cases, when you gotta check rapidly if your calculation seems correct, look at the digit number.

Let $X=x*10+a$ and $Y=y*10+b$

$XY=(ay+x+bx+y)*10+ab$

Hence the unit digit of XY will be the unit digit of ab, which is easier to get.

For example :

$46 \times 73$

Here, $a=6$ and $b=3$ . So $ab=1{\color{blue} 8}$
Hence the unit digit of $46 \times 73$ is ${\color{blue} 8}$
If you find a result whose digit number is not 8, you can directly calculate again.

Here is only a beginning for cubic roots... And shall be known

$1^3={\color{red}1}$
$2^3={\color{red}8}$
$3^3=2{\color{red}7}$
$4^3=6{\color{red}4}$
$5^3=12{\color{red}5}$
$6^3=21{\color{red}6}$
$7^3=34{\color{red}3}$
$8^3=51{\color{red}2}$
$9^3=72{\color{red}9}$
$10^3=100{\color{red}0}$

Notice that each number appears once in the unit digit.

This means that if, for example, you're looking for the cubic root of a number whose unit digit is 6, its cubic root necessarily ends with a 6.