Simplify Square Root Expression: (√12 × √4 × √3)/(√2 × √2)

To solve this problem, we'll follow these steps:

• Simplify the numerator by multiplying the square roots together.
• Simplify the denominator by recognizing that $\sqrt{2} \times \sqrt{2}$ equals 2.
• Apply the quotient rule for square roots to simplify the expression.

Now, let's work through each step:
Step 1: The numerator is $\sqrt{12} \cdot \sqrt{4} \cdot \sqrt{3}$. Using the product property, combine them into one square root:
$\sqrt{12 \times 4 \times 3} = \sqrt{144}$.

Step 2: The denominator is $\sqrt{2} \cdot \sqrt{2} = \sqrt{4} = 2$.

Step 3: Now apply the quotient rule:
$\frac{\sqrt{144}}{2} = \sqrt{\frac{144}{4}} = \sqrt{36}$.

The result of $\sqrt{36}$ is 6.

Therefore, the solution to the problem is $6$.