3/3/9 Happy Square Root Day
\_ This morning some guy on KCBS AM 740 was playing with this and said
something like "if you take the square root of every number, they
don't look so big anymore. For example, next week the square root
of my age is just 8. And the square root of the $838 billion
stimulus package is just $29 billion."
No wonder American kids rank last in math among industrialized
countries.
\_ i think the sqrt of his iq is also 8.
\_ Dude needs to go back to school, and age 8 seems like a good
time to learn about square roots.
\_ Huh? I don't see anything wrong with his statement.
\_ sqrt(838e9) is about 915423.
\_ I guess. sqrt(838) =~ 29. (Billion dollars) is the
units. Depends on how you look at it.
\_ Right, but you need to square root the units too,
just like sqrt(10000 m^2) = 100 m. The answer is
the same whether you consider the units to be m^2
or (10000 m^2) or whatever.
\_ I understand this, but what is the square
root of "2 dollars"? This is like asking what
is the square root of "2 cows". The original
statement said "square root of every number"
and not "square root of every quantity". You
could argue (correctly) that 838,000,000,000
is a number in itself and its root is not
29,000,000,000, but what about "838 cows"? What
is the square root of a cow? I think the key
number is 838 and not 838*(units). You have
to be pretty pedantical to not realize that.
\_ If your units are billions of dollars than
your square root units of ~ 31622 * $^(1/2).
sqrt (838) * sqrt (1,000,000,000) ~=
29 * 31622 ~=
915422
\_ 915422 *what*? Not dollars.
\_ $^(1/2) Which is 1/31622 of
(Billion $)^(1/2)
\_ Exactly, which is nonsense. So
ignore the units.
\_ If you ignore the units you can
turn it anything you want.
Sqrt($838e9) = $838e9 if my
units are "$838e9" and I've
decided units are meaningless.
\_ You have to use some common
sense here. The square root
of his age (64) is 8, not
8 (years)^1/2.
\_ But by your logic we can
make the units billions of
years, and now the the
square root of 64 is
252982.
Better example: the square root of $1 is 1 if
you are ignoring units, but the square root
of 100 pennies is 10! 100 pennies = 1 dollar
so how can those two be different.
$1 = 100c
sqrt($1) = sqrt(100c)
1 * $^(1/2) = 10 * c^(1/2)
The difference is in the units. 1 c^(1/2)
is, by definition, 1/10th of 1 $^(1/2).
\_ But what is a sqrt($)? or a sqrt(cent)?
\_ I guess you're right. Square rooting a number
independently of its unit like this makes no
sense, but it is what the original statement
said, and really it doesn't sound like he was
trying to make sense anyway. (FWIW, I think
sqrt("2 cows") is meaningless too, unless you
can come up with a meaning for 1.4 cow^(1/2).)
\_ Depends on how good you are at math, actually. |