Simplify
\[ \sqrt{3 – 2\sqrt{2}} \]
Solution:
\[ \sqrt{3 – 2\sqrt{2}} = \sqrt{a} – \sqrt{b} \]
\[ (\sqrt{a} – \sqrt{b})^2 = a + b – 2\sqrt{ab} \]
\[ a + b = 3, \quad 2\sqrt{ab} = 2\sqrt{2} \Rightarrow ab = 2 \]
\[ a = 2, \quad b = 1 \]
\[ \therefore \sqrt{3 – 2\sqrt{2}} = \sqrt{2} – \sqrt{1} \]
\[ = \sqrt{2} – 1 \]