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

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

Re: Simplifying radicals

if you mean ...

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

then ...

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

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

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

Re: Simplifying radicals

skeeter said:

if you mean ...

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

then ...

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

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

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

Click to expand...

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

Re: Simplifying radicals

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

Re: Simplifying radicals

Oh Ok,

I see now, thanks a lot for replying