Toutatis wrote:

I struggled on solving so I used trick :

1st - convert the square root of 500 in decent form : (5 + 5√5)/(10 + 10√5)

2nd - Factorise 5 in numerator and denominator : 5*(1+√5) / 5*(2+2√5)

You end up with the following expression : 1+√5 / 2+2√5

Now if you look at the answer choices, there's only one that holds value between 0 and 1 (1/2-answer A).

Looking again at the expression, you can see that it cannot be above 1, so answer A it is.

If you have: \(\frac{5 + 5√5}{10 + 10√5}\), you can factorise:

Numerator: \(1*(5 + 5√5)\)

Denominator: \(2*(5 + 5√5)\).

So you have \(\frac{1*(5 + 5√5)}{2*(5 + 5√5)}\) \(=\frac{1}{2}\)

Hope it helps.

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