Simplify the expression $\sqrt{6 - 2\sqrt{5}}$.

1. Problem Description

Simplify the expression $\sqrt{6 - 2\sqrt{5}}$.

2. Solution Steps

We are looking for two numbers, $a$ and $b$, such that

$(a-b)^2 = a^2 + b^2 - 2ab = 6 - 2\sqrt{5}$.

Therefore, we need to find $a$ and $b$ such that $a^2 + b^2 = 6$ and $ab = \sqrt{5}$.

We can deduce that $a^2b^2 = 5$. Let's assume $a = \sqrt{5}$ and $b = 1$. Then

$a^2 + b^2 = (\sqrt{5})^2 + 1^2 = 5 + 1 = 6$.

So, we can write $6 - 2\sqrt{5} = (\sqrt{5} - 1)^2$.

Then we have:

$\sqrt{6 - 2\sqrt{5}} = \sqrt{(\sqrt{5} - 1)^2} = |\sqrt{5} - 1|$.

Since $\sqrt{5} > 1$, we have $|\sqrt{5} - 1| = \sqrt{5} - 1$.

3. Final Answer

$\sqrt{5} - 1$