# distance

• Sep 1st 2007, 12:41 AM
deathtolife04
distance
i'm trying to find the distance from (2,-7) to (5,1)

i used the distance formula and got down to d=√(9+64)

9+64=73, which obviously isn't a perfect square.

9 and 64, however, ARE perfect squares

sooo, is there a way i can use 3 and 8 to figure this out?

or is my answer just gonna be
√73

????
• Sep 1st 2007, 12:58 AM
qbkr21
Re:
Re:
• Sep 1st 2007, 06:02 AM
Soroban
Hello, deathtolife04!

Quote:

i'm trying to find the distance from (2,-7) to (5,1)

i used the distance formula and got down to $\displaystyle d \,=\, \sqrt{9+64}$

$\displaystyle 9+64\,=\,73$, which obviously isn't a perfect square.

9 and 64, however, ARE perfect squares

sooo, is there a way i can use 3 and 8 to figure this out? . . . . no

or is my answer just gonna be $\displaystyle \sqrt{73}$ ? . . . . yes

This is a common thought . . . I wondered it about it myself (years ago).
. . Then I took a closer look . . .

The Distance Formula is: .$\displaystyle d \;=\;\sqrt{\underbrace{(x_2-x_1)^2} + \underbrace{(y_2-y_1)^2}}$
. . . . . . . . . . . . . . . . . . . . . . . . . .$\displaystyle \uparrow$ . . . . . . $\displaystyle \uparrow$
. . . . . . . . . . . . . . . . . . . . . . . .
square! . . .square!

Get it? .We will always have two squares under the square root.

The urge to "simplify" will always be there.

But in general, $\displaystyle \sqrt{a^2+b^2}$ is not equal to $\displaystyle a+b$.

So we must wholeheartedly resist the temptation to "simplify", say, $\displaystyle \sqrt{16 + 25}$

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Personally, I think it's a dirty trick . . . daring us to blunder.

I've accepted other injustices . . .
. . that the word 'monosyllabic' has five syllables
. . that the word 'lisp' has an 's' in it.

So I've learned to cope with the dangerous Distance Formula.