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.