Simplifying radicals: 2 * 5(sqrt) / 5(sqrt) - 3

skaterchicky23

New member
Joined
May 4, 2008
Messages
8
I have a question of 2 * 5(sqrt)
-------------
5(sqrt)-3

I took this problem and took the following steps:

2*5(sqrt) 5(sqrt)+3
---------- * -----------
5(sqrt)-3 5(sqrt)+3

and got an answer of

2(5+3)
------
(-3)^2+(5(sqrt)^2

=16 8
------- or ---
34 17

is this correct?

I have tried looking up online for what else I would do instead, but the examples are showing similar to this.

Please help
 

skeeter

Senior Member
Joined
Dec 15, 2005
Messages
2,396
Re: Simplifying radicals

if you mean ...

\(\displaystyle \frac{2 \sqrt{5}}{\sqrt{5} - 3}\)

then ...

\(\displaystyle \frac{2 \sqrt{5}}{\sqrt{5} - 3} \cdot \frac{\sqrt{5} + 3}{\sqrt{5} + 3} =\)

\(\displaystyle \frac{10 + 6\sqrt{5}}{5 - 9} =\)

\(\displaystyle - \frac{5 + 3\sqrt{5}}{2}\)
 

skaterchicky23

New member
Joined
May 4, 2008
Messages
8
Re: Simplifying radicals

skeeter said:
if you mean ...

\(\displaystyle \frac{2 \sqrt{5}}{\sqrt{5} - 3}\)

then ...

\(\displaystyle \frac{2 \sqrt{5}}{\sqrt{5} - 3} \cdot \frac{\sqrt{5} + 3}{\sqrt{5} + 3} =\)

\(\displaystyle \frac{10 + 6\sqrt{5}}{5 - 9} =\)

\(\displaystyle - \frac{5 + 3\sqrt{5}}{2}\)

HI, thanks for replying,

How do you get the 10 in the 3rd equation?
I'm confused by how the 10 became part of the equation, if you could explain that would be great
 

skeeter

Senior Member
Joined
Dec 15, 2005
Messages
2,396
Re: Simplifying radicals

\(\displaystyle 2\sqrt{5} \cdot \sqrt{5} = 2(\sqrt{5} \cdot \sqrt{5}) = 2(5) = 10\)
 

skaterchicky23

New member
Joined
May 4, 2008
Messages
8
Re: Simplifying radicals

Oh Ok,

I see now, thanks a lot for replying
 
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