1. **State the problem:** Rationalise the denominator of the expression $\frac{6}{\sqrt{10}}$ and simplify the result. 2. **Formula and rule:** To rationalise a denominator containing a square root, multiply numerator and denominator by the same square root to eliminate the root in the denominator. 3. **Apply the rule:** Multiply numerator and denominator by $\sqrt{10}$: $$\frac{6}{\sqrt{10}} \times \frac{\sqrt{10}}{\sqrt{10}} = \frac{6 \sqrt{10}}{(\sqrt{10})^2}$$ 4. **Simplify the denominator:** Since $(\sqrt{10})^2 = 10$, the expression becomes: $$\frac{6 \sqrt{10}}{10}$$ 5. **Simplify the fraction:** Divide numerator and denominator by 2: $$\frac{3 \sqrt{10}}{5}$$ 6. **Final answer:** The rationalised and simplified form is $\frac{3 \sqrt{10}}{5}$.