Simplify the Expression: (√8/2√16) × (√64/√2√4)

Look for perfect square factors! For example, $\sqrt{8} = \sqrt{4 \cdot 2} = 2\sqrt{2}$ because 4 is a perfect square. Always break down numbers into their prime factors first.

When you multiply $\frac{\sqrt{2}}{4} \cdot \frac{4}{\sqrt{2}}$, the 4's cancel out and the $\sqrt{2}$'s cancel out, leaving you with $\frac{1}{1} = 1$!

Technically yes, but it's much harder! You'll get messy expressions like $\frac{\sqrt{8} \cdot \sqrt{64}}{2\sqrt{16} \cdot \sqrt{2} \cdot \sqrt{4}}$. Always simplify radicals first to make the arithmetic easier.

Double-check your radical simplifications! Common errors include forgetting that $\sqrt{16} = 4$ (not 8) or that $\sqrt{8} = 2\sqrt{2}$ (not just $\sqrt{8}$).

In this problem, the final answer is 1, so no rationalization needed! But if your final answer had a radical in the denominator, then yes, you should rationalize it.