1. **State the problem:** Rationalise the denominator of $$\frac{15 + \sqrt{5}}{6\sqrt{5}}$$ and simplify the expression. 2. **Formula and rule:** To rationalise a denominator containing a square root, multiply numerator and denominator by the conjugate or the radical itself to eliminate the root in the denominator. 3. **Multiply numerator and denominator by $$\sqrt{5}$$:** $$\frac{15 + \sqrt{5}}{6\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}} = \frac{(15 + \sqrt{5})\sqrt{5}}{6 \times 5}$$ 4. **Simplify numerator:** $$ (15 + \sqrt{5})\sqrt{5} = 15\sqrt{5} + (\sqrt{5})^2 = 15\sqrt{5} + 5 $$ 5. **Simplify denominator:** $$ 6 \times 5 = 30 $$ 6. **Write the expression:** $$ \frac{15\sqrt{5} + 5}{30} $$ 7. **Factor numerator:** $$ 15\sqrt{5} + 5 = 5(3\sqrt{5} + 1) $$ 8. **Simplify the fraction:** $$ \frac{5(3\sqrt{5} + 1)}{30} = \frac{3\sqrt{5} + 1}{6} $$ **Final answer:** $$ \frac{3\sqrt{5} + 1}{6} $$