12. Rationalise the denominator of \[ \frac{12}{7 \sqrt{3}} \]

To rationalise the denominator of \(\frac{12}{7 \sqrt{3}}\), we need to eliminate the square root from the denominator. To do this, we multiply both the numerator and the denominator by \(\sqrt{3}\): \[ \frac{12 \cdot \sqrt{3}}{7 \sqrt{3} \cdot \sqrt{3}} = \frac{12 \sqrt{3}}{7 \cdot 3} = \frac{12 \sqrt{3}}{21} \] Now, we can simplify it further by dividing both the numerator and the denominator by 3: \[ \frac{4 \sqrt{3}}{7} \] And there you have it! The rationalised form of \(\frac{12}{7 \sqrt{3}}\) is \(\frac{4 \sqrt{3}}{7}\).