# surds

• Sep 14th 2009, 10:31 AM
maplematt
surds
Hey, I'm really struggling with a question on my maths homework.

Express root5 +3/root 5 -2 in the form Proot5 + Q where P and Q are integers

I got 2root5

Is this right?
• Sep 14th 2009, 11:18 AM
e^(i*pi)
Quote:

Originally Posted by maplematt
Hey, I'm really struggling with a question on my maths homework.

Express root5 +3/root 5 -2 in the form Proot5 + Q where P and Q are integers

I got 2root5

Is this right?

I get $\displaystyle 4\sqrt{5} - 2$

It seems to be addition, don't let the surd fool you, it's like x+x = 2x
• Sep 14th 2009, 11:20 AM
maplematt
Quote:

Originally Posted by e^(i*pi)
I get $\displaystyle 4\sqrt{5} - 2$

It seems to be addition, don't let the surd fool you, it's like x+x = 2x

do you mind explaining how you got to that?
• Sep 14th 2009, 11:28 AM
e^(i*pi)
Quote:

Originally Posted by maplematt
do you mind explaining how you got to that?

I could have misread the OP but I don't think so.

Let $\displaystyle u = \sqrt{5}$ so that the equation becomes $\displaystyle u + 3u - 2$

What I did was said that you can combine the u terms to give $\displaystyle 4u - 2$

And since $\displaystyle u = \sqrt{5}$ we get $\displaystyle 4\sqrt{5} - 2$

$\displaystyle 4$ and $\displaystyle -2$ are both integers so it does satisfy the terms
• Sep 14th 2009, 11:31 AM
maplematt
Quote:

Originally Posted by e^(i*pi)
I could have misread the OP but I don't think so.

Let $\displaystyle u = \sqrt{5}$ so that the equation becomes $\displaystyle u + 3u - 2$

What I did was said that you can combine the u terms to give $\displaystyle 4u - 2$

And since $\displaystyle u = \sqrt{5}$ we get $\displaystyle 4\sqrt{5} - 2$

$\displaystyle 4$ and $\displaystyle -2$ are both integers so it does satisfy the terms

Thanks for the continued help,but I think you've misread, or maybe i didn't qrite it properly.

root5 +3/root 5 -2

(root5 plus 3) divided by (root 5 minus 2)

sorry if i caused some confusion.
• Sep 14th 2009, 11:39 AM
masters
Quote:

Originally Posted by maplematt
Thanks for the continued help,but I think you've misread, or maybe i didn't qrite it properly.

root5 +3/root 5 -2

(root5 plus 3) divided by (root 5 minus 2)

sorry if i caused some confusion.

Hi maplematt,

$\displaystyle \frac{\sqrt{5}+3}{\sqrt{5}-2}\cdot \frac{\sqrt{5}+2}{\sqrt{5}+2}=\frac{5+5\sqrt{5}+6} {5-4}=11+5\sqrt{5}$
• Sep 14th 2009, 11:45 AM
e^(i*pi)
Quote:

Originally Posted by maplematt
Thanks for the continued help,but I think you've misread, or maybe i didn't qrite it properly.

root5 +3/root 5 -2

(root5 plus 3) divided by (root 5 minus 2)

sorry if i caused some confusion.