\( \frac{2}{\sqrt{2}} \) Rationalize the denominator and simplify.

To rationalize the denominator of \( \frac{2}{\sqrt{2}} \), multiply both the numerator and the denominator by \( \sqrt{2} \): \[ \frac{2}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{2\sqrt{2}}{2} \] Now, simplify the fraction: \[ \frac{2\sqrt{2}}{2} = \sqrt{2} \] So, \( \frac{2}{\sqrt{2}} \) simplifies to \( \sqrt{2} \). Rationalizing the denominator is a clever trick that helps avoid messy calculations or interpretations, especially in fields like engineering where precise measurements are vital. It ensures expressions are in a more standard form, making them easier to work with and compare. When working on problems like this, a common mistake is to forget to multiply both the top and bottom by the same number, which can lead to incorrect results. Always remember to keep the fraction equivalent!