d) \( \frac{\sqrt{16}-\sqrt{64}}{\sqrt{2}} \)

To solve the expression \( \frac{\sqrt{16} - \sqrt{64}}{\sqrt{2}} \), we first simplify the square roots. We know that \( \sqrt{16} = 4 \) and \( \sqrt{64} = 8 \). Substituting these values in gives us \( \frac{4 - 8}{\sqrt{2}} = \frac{-4}{\sqrt{2}} \). To rationalize the denominator, we multiply the numerator and denominator by \( \sqrt{2} \), resulting in \( \frac{-4\sqrt{2}}{2} = -2\sqrt{2} \). Now you've got -2√2, a neat result! Did you know that simplifying square roots can be like finding hidden treasures in math? Each time you break it down, you uncover a new layer of knowledge, just like archaeological digs reveal historical artifacts! Want to dig deeper? Whenever you're working with square roots, ensure your calculations are precise. A common mistake is misidentifying square roots or rushing through simplification; always double-check your steps! Math can be tricky, but slowing down can quickly save you from silly errors! Keep practicing, and you'll be a square root superstar in no time!