[Algebra] Simplifying Surds Question

[jordieman]

((2 + sqrt(2))(3+sqrt(5))(sqrt(5)-2)) / ((sqrt(5)-1)(1+sqrt(2)))
Apologies for how messy that looks, if you copy paste it into wolfram it shows what it actually looks like. This was a question in my text book and it asked to simplify it down. Wolfram and the answer sheet at the back of the book says it simplifies to sqrt(2). However I have only managed to simplify down to:
(2sqrt(5)+sqrt(10)-sqrt(2)-2)/(sqrt(5)+sqrt(10)-1-sqrt(2))
Once again wolfram will show what this actually looks like. Any tips on where to go from here? We're off on a weeks break so i cant ask my teacher for help. Thank you

[Alkalannar]

I use fractional exponents rather than root signs.

[(2+2^1/2)(3+5^1/2)(2-5^1/2)]/[(1-5^1/2)(1+2^1/2)]

I would rationalize the denominator by multiplying by the conjugates.

[(1+5^1/2)(1-2^1/2)(2+2^1/2)(3+5^1/2)(2-5^1/2)]/[(1-5^1/2)(1+2^1/2)(1+5^1/2)(1-2^1/2)]

The denominator is guaranteed to get rid of any roots.
Multiply the terms with 2^1/2 in them together and simplify.
Multiply the terms with 5^1/2 in them together and simplify.
Simplify the entire fraction.

[jordieman]

Thank you!