Question: Rationalise the denominator of $\frac{15}{\sqrt{5}}$
Give your answer in its simplest form.
1. **State the problem:** We need to rationalise the denominator of the expression $$\frac{15}{\sqrt{5}}$$ and simplify the result.
2. **Recall the 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. **Multiply numerator and denominator by $\sqrt{5}$:**
$$\frac{15}{\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}} = \frac{15 \times \sqrt{5}}{\sqrt{5} \times \sqrt{5}}$$
4. **Simplify the denominator:**
$$\sqrt{5} \times \sqrt{5} = 5$$
5. **Substitute back:**
$$\frac{15 \times \sqrt{5}}{5}$$
6. **Simplify the fraction by dividing numerator and denominator by 5:**
$$\frac{\cancel{15}^3 \times \sqrt{5}}{\cancel{5}^1} = 3 \sqrt{5}$$
7. **Final answer:**
$$3 \sqrt{5}$$
This is the simplest form with a rationalised denominator.