We will simplify the given expression step by step:

$\frac{4\sqrt{12}}{3\sqrt{4}}$

Step 1: Simplify Square Roots

• $\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}$.
• $\sqrt{4} = 2$.

Now, substituting these values into the expression:

$\frac{4(2\sqrt{3})}{3(2)}$

Step 2: Simplify the Expression

$\frac{8\sqrt{3}}{6}$

Since both numerator and denominator are divisible by 2:

$\frac{4\sqrt{3}}{3}$

Final Answer:

$\frac{4\sqrt{3}}{3}$

Would you like a more detailed breakdown or have any questions?

Here are five related problems to try:

1. Simplify $\frac{5\sqrt{18}}{2\sqrt{2}}$.
2. Evaluate $\frac{6\sqrt{27}}{3\sqrt{9}}$.
3. Simplify $\frac{\sqrt{50}}{\sqrt{2}}$.
4. Rationalize and simplify $\frac{8}{\sqrt{5}}$.
5. Simplify $\frac{10\sqrt{8}}{4\sqrt{2}}$.

Tip:

When simplifying square roots, look for perfect square factors to break them down easily.