Rationalise the denominator of \[ \frac{15}{\sqrt{5}} \]

To rationalise the denominator of \(\frac{15}{\sqrt{5}}\), you multiply both the numerator and the denominator by \(\sqrt{5}\). This gives you: \[ \frac{15 \cdot \sqrt{5}}{\sqrt{5} \cdot \sqrt{5}} = \frac{15\sqrt{5}}{5}. \] Now, simplify the fraction: \[ \frac{15\sqrt{5}}{5} = 3\sqrt{5}. \] So, the rationalised form of \(\frac{15}{\sqrt{5}}\) is \(\mathbf{3\sqrt{5}}\). For anyone working with radical expressions, this is a handy trick! It not only makes your expression neater but also prepares it for further mathematical operations. Remember, rationalisation is especially useful when dealing with fractions in long division or when trying to simplify square roots in equations. Math isn’t just about numbers; it has a rich history too! The practice of rationalising denominators became common during the Islamic Golden Age, where scholars, including Al-Khwarizmi, made significant strides in algebra and number theory. This transformed the way we handle roots, laying the groundwork for modern mathematics. Isn’t it fascinating how our mathematical processes are linked to such a vibrant history?