Multiply Square Roots: Solving √(2/4) × √6 Step by Step

To solve the expression $\sqrt{\frac{2}{4}} \cdot \sqrt{6}$, we will break it down and simplify step by step.

Step 1: Simplify the square root of the fraction.
$\sqrt{\frac{2}{4}}$ can be rewritten using the square root of a quotient property:
$\sqrt{\frac{2}{4}} = \frac{\sqrt{2}}{\sqrt{4}}$.

Step 2: Simplify $\sqrt{4}$.
Since $\sqrt{4} = 2$, the expression becomes:
$\frac{\sqrt{2}}{2}$.

Step 3: Multiply by $\sqrt{6}$.
Now multiply $\frac{\sqrt{2}}{2}$ by $\sqrt{6}$:
$\frac{\sqrt{2}}{2} \cdot \sqrt{6} = \frac{\sqrt{2 \cdot 6}}{2}$.

Step 4: Simplify the square root.
The multiplication inside the square root becomes $\sqrt{12}$, so:
$\frac{\sqrt{12}}{2}$.

Step 5: Simplify $\sqrt{12}$.
Since $\sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3}$,
this results in $\frac{2\sqrt{3}}{2} = \sqrt{3}$.

Therefore, the solution to the problem is $\sqrt{3}$.