Gmat_mission wrote:$$\frac{5+5\sqrt{5}}{10+\sqrt{500}}=$$
A) \(\frac{1}{2}\)
B) \(2\)
C) \(1 + \sqrt{5}\)
D) \(1 + 5\sqrt{5}\)
E) \(5 + \sqrt{5}\)

[spoiler]OA=A[/spoiler]

Source: Veritas Prep

We have $$\frac{5+5\sqrt{5}}{10+\sqrt{500}}$$
$$\frac{5(1+\sqrt{5})}{10+\sqrt{5\times100}}$$
$$\frac{5(1+\sqrt{5})}{10+\sqrt{5\times10^2}}$$
$$\frac{5(1+\sqrt{5})}{10+10\sqrt{5}}$$
$$\frac{5(1+\sqrt{5})}{10(1+\sqrt{5})}$$
\(\frac{1}{2}\)

The correct answer: A

Hope this helps!

-Jay
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