Distance Formula

• Aug 25th 2010, 09:19 PM
GLAMX
Distance Formula
I'm really having a hard time with this. It deals with distance formula.

http://i35.tinypic.com/2j5hztf.jpg

As you can see from that picture, I tried solving the problem and got 117 as an answer. But my teacher told me the answer was 3√13 but I have no idea how.

Please elaborately explain to me how I could arrive to the correct answer. Thank You
• Aug 25th 2010, 09:30 PM
pickslides
$\displaystyle \sqrt{117}= \sqrt{9\times 13} = \sqrt{9}\sqrt{ 13}= 3\sqrt{ 13}$
• Aug 25th 2010, 09:35 PM
Quote:

Originally Posted by GLAMX
I'm really having a hard time with this. It deals with distance formula.

http://i35.tinypic.com/2j5hztf.jpg

As you can see from that picture, I tried solving the problem and got 117 as an answer. But my teacher told me the answer was 3√13 but I have no idea how.

Please elaborately explain to me how I could arrive to the correct answer. Thank You

Actually sqrt(117) = 3*sqrt(13). However, although it is correct, it is not in the form the teacher expects. You need to factor out squares when possible. It's actually not that bad. You probably will only need to check 1, 4, 9, 16, 25, 36, 49 anyway.

Now, 117 = 9 * 13, so
sqrt(117) = sqrt(9*13)

but. we know sqrt(a*b) = sqrt(a)sqrt(b) [exponent rule], so

sqrt(9*13) = sqrt(9)*sqrt(13) = 3 * sqrt(13), and we are done.
• Aug 25th 2010, 10:11 PM
GLAMX
Quote:

Originally Posted by pickslides
$\displaystyle \sqrt{117}= \sqrt{9\times 13} = \sqrt{9}\sqrt{ 13}= 3\sqrt{ 13}$

Thank you. This was very helpful. Just one more question, the 9 and 13, does it have to be those specific numbers? Or can they be two numbers that equal to 117?
• Aug 25th 2010, 10:17 PM
pickslides
You have to find a factor of 117 that is a square number.

I.e. $\displaystyle 1^2 = 1, 2^2 = 4, 3^2= 9 , 4^2=16, \dots$

Factoring into 2 numbers that aren't square will not have the desired affect.