# Distance Formula with Roots

• Nov 17th 2007, 01:47 PM
FactoringAnguish
Distance Formula with Roots
Hey guys! I'm having problems with some problems regarding the distance formula and I am thoroughly stumped, so I kindly ask for help please. I'm fine solving distance without roots but when the roots came in I became lost.
*don't know how to do the square root symbol on here so I will just put, a "*" before the square roots.

1) (0, -*3) and (*5, 0)
Square Roots: negative square root of 3 (the negative is on the outside), and square root of 5

2) (3*3, *5) and (-*3, 3*5)
Square Roots: (3 square root of 3, square root of 5) and (negative square root of 3, 3 square root of 5) Sorry about the lack of square root symbol! Thanks!
• Nov 17th 2007, 02:55 PM
bobak
for the first one you're trying to find the distance between the points $\displaystyle \left( 0,-\sqrt{3} \right)$ and $\displaystyle \left( \sqrt{5},0 \right)$.

All you have to do is use pythagorus' theorem, you form a right angled triangle with sides of length $\displaystyle \sqrt{3}$ and $\displaystyle \sqrt{5}$ find out the length of the hypotenuse (and hence the distance between the points)

$\displaystyle d^2 = {\sqrt{3}}^2 + {\sqrt{5}}^2$ so $\displaystyle d^2 = 3 + 5$
$\displaystyle d^2 = 8$
$\displaystyle d= 2\sqrt{2}$