Find the value
\[ \sqrt{3 – 2\sqrt{2}} \]
(a) \(\sqrt{2} – 1\) \quad (b) \(\sqrt{2} + 1\) \quad (c) \(\sqrt{3} – \sqrt{2}\) \quad (d) \(\sqrt{3} + \sqrt{2}\)
Solution:
\[ \sqrt{3 – 2\sqrt{2}} = \sqrt{a} – \sqrt{b} \]
\[ (\sqrt{a} – \sqrt{b})^2 = a + b – 2\sqrt{ab} \]
\[ a + b = 3,\quad ab = 2 \Rightarrow a = 2,\ b = 1 \]
\[ \therefore \sqrt{3 – 2\sqrt{2}} = \sqrt{2} – 1 \]
\[ \therefore \text{Correct Answer: } \sqrt{2} – 1 \ (\text{Option a}) \]