16. Rationalise the denominator of \[ \frac{8}{\sqrt{2}} \]

To rationalize the denominator of \(\frac{8}{\sqrt{2}}\), you can multiply both the numerator and the denominator by \(\sqrt{2}\). This gives you: \[ \frac{8 \cdot \sqrt{2}}{\sqrt{2} \cdot \sqrt{2}} = \frac{8\sqrt{2}}{2} \] Now, simplify the expression: \[ \frac{8\sqrt{2}}{2} = 4\sqrt{2} \] So, the rationalized form of \(\frac{8}{\sqrt{2}}\) is \(4\sqrt{2}\). The magic of rationalizing the denominator not only makes expressions neater but also is rooted in a mathematical convention that helps prevent messy calculations, especially when you're solving more complex problems in algebra or calculus. Embracing these practices can help make your math journey smoother and more enjoyable! This technique has historical significance as well; rationalization dates back to ancient civilizations, including the Greeks and Indians, who devised ways to simplify irrational numbers for more straightforward mathematical handling. By mastering it, you connect with mathematicians of the past, keeping their techniques alive in your modern calculations!