distance formula: Find distance between (-1, 2), (5, 4)

[unregistered]

Hi folks, I have a different result than my text book has and I was hoping that someone could clear this up?

The question aks: Find the distance between the points (-1, 2), (5, 4).

√(5 - (-1))^2 + (4 - 2)^2
(original equation)

√(5 + 1)^2 + (4 - 2)^2
(-(-1) becomes positive yes?)

√6^2 + 2^2
(solve for the items within parentheses first)

√36 + 4

I get the following below:
√40 ≈ 6.32

The book shows the following however:
2√10

I don't understand the books result, can anyone clarify?

Thank-you very much.

Nicholas.

 

[skeeter]

\(\displaystyle \L \sqrt{40} = \sqrt{4*10} = \sqrt{4}*\sqrt{10} = 2\sqrt{10}\)

 

[unregistered]

Hey thanks alot skeeter. I guess I don't know when I would just multiply 4 times 10 and if I was going to do that, why I wouldn't I leave it √2 √10? I guess I'm a little closer to knowing why so that's cool, thanks again.

sorry about the heading, I don't remember putting it up there like that, I would never just write "find....". Sorry if I did unintentionally.[/tex]

 

[jonboy]

Hey, Unregistered!


Here is how I remember to simplify \(\displaystyle \L \,\sqrt{40}\)


Remember this:\(\displaystyle \L \;\sqrt{x}\bullet\sqrt{x}\,=\,x\)


First simplify:\(\displaystyle \L \;\sqrt{40}\,=\,\sqrt{10\bullet 4}\,=\,\sqrt{10\bullet 2\bullet 2}\)


So since \(\displaystyle \L \;\sqrt{2}\bullet\sqrt{2}\,=\,2\,\) and we have \(\displaystyle \L \,\sqrt{10}\,\)left:\(\displaystyle \L \;2\sqrt{10}\)

 

[unregistered]

Aha, I totally get it now. When simplifying a square root, I'm trying to find 2 numbers that I can multiply together to make the original square root, which in this case are:

√4 • √10

But not:

√5 • √8

because I want one of the numbers to make a perfect square and 4 fits that bill:

√4 = 2

Then I take the number (2) and that becomes the root index and √10 stays because it cannot be broken down any further, so:

2√10

Awesome, thanks alot for the help. Now I have to tackle completing the square to sketch a circle so I may be back b/c I can't seem to wrap my peanut brain around that.

thanks again.