Find the denominator after rationalisation
\[ \frac{7}{3\sqrt{3} – 2\sqrt{2}} \]
Solution:
\[ \frac{7}{3\sqrt{3} – 2\sqrt{2}} \times \frac{3\sqrt{3} + 2\sqrt{2}}{3\sqrt{3} + 2\sqrt{2}} \]
\[ = \frac{7(3\sqrt{3} + 2\sqrt{2})}{(3\sqrt{3})^2 – (2\sqrt{2})^2} \]
\[ = \frac{7(3\sqrt{3} + 2\sqrt{2})}{27 – 8} \]
\[ = \frac{7(3\sqrt{3} + 2\sqrt{2})}{19} \]
\[ \therefore \text{Denominator} = 19 \]