Multiply Square Roots: Calculate √(2/4) × √(8/16)

To solve the given exercise, let's simplify each square root expression separately:

• Step 1: Simplify $\sqrt{\frac{2}{4}}$.

  The fraction $\frac{2}{4}$ simplifies to $\frac{1}{2}$. Thus, $\sqrt{\frac{2}{4}} = \sqrt{\frac{1}{2}} = \frac{\sqrt{1}}{\sqrt{2}} = \frac{1}{\sqrt{2}}$.

• Step 2: Simplify $\sqrt{\frac{8}{16}}$.

  The fraction $\frac{8}{16}$ simplifies to $\frac{1}{2}$. Thus, $\sqrt{\frac{8}{16}} = \sqrt{\frac{1}{2}} = \frac{\sqrt{1}}{\sqrt{2}} = \frac{1}{\sqrt{2}}$.

• Step 3: Multiply the results from Step 1 and Step 2.

  $\sqrt{\frac{2}{4}} \cdot \sqrt{\frac{8}{16}} = \frac{1}{\sqrt{2}} \cdot \frac{1}{\sqrt{2}} = \frac{1 \cdot 1}{\sqrt{2} \cdot \sqrt{2}} = \frac{1}{2}$.

Therefore, the solution to the given expression is $\frac{1}{2}$.