Calculating Distance Between Two Points: Simplifying Radical Expressions

[Xavier]

First I'd like to say that I'm getting back into college after several years out in the job market. Unfortunately, I need to complete several more upper division math courses before I can complete my CS degree. Before I go back and start taking my classes again, I've been trying to self-study my way back through Calc I, and having difficulty just getting beyond the first section. Maybe I just need to refamiliarize myself with the basics.

What has me stuck is determining the distance between two points. Pretty simple. I understand the theory, and can work the problems well, until I got to this one, and I've been stuck.

Determine the distance between two points:
(1,√3), (-1,1)

My book shows the answer as:
√(8-2√3)

(I'm at work, I'll need to verify this, but 99% sure this is what the book states. I do know the question is 100% correct.)

When I apply the distance formula:
√((X2-X1)^2+(Y2-Y1)^2)

I get:
√((-1-1)^2+(1-√3)^2)

When I reduce this I get:
√(4+(1-√3)^2)

Am I not reducing this far enough? If so, how do you reduce down to √(8-2√3)?

Thanks for your help and patience!

 

[pig]

When I reduce this I get:
√(4+(1-√3)^2)

Am I not reducing this far enough? If so, how do you reduce down to √(8-2√3)?

Just calculate the square:

√(4+(1-√3)^2)

= √(4+(1-√3)(1-√3))

= √(4+1-2√3+3)

= √(8-2√3)

 

[Xavier]

Thank you! Makes sense to me now. I know it seems basic, but I suppose this is where I have the most difficult time.. knowing where to use what to get the most simple answer.

Thanks again for your help!