To simplify $\sqrt{12}$ by removing all perfect squares from inside the square root, let's break it down:

1. Identify any perfect square factors of 12.

   • $12 = 4 \times 3$
   • Since 4 is a perfect square ($4 = 2^2$), we can rewrite $\sqrt{12}$ as: $\sqrt{12} = \sqrt{4 \times 3}$

2. Apply the property of square roots that states $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$: $\sqrt{12} = \sqrt{4} \times \sqrt{3}$

3. Simplify $\sqrt{4}$ to 2: $\sqrt{12} = 2 \sqrt{3}$

Thus, the simplified form is: $\sqrt{12} = 2\sqrt{3}$

Would you like more details or have any questions?

Here are five related questions to explore this concept further:

1. How would you simplify $\sqrt{18}$?
2. Can you explain why $\sqrt{4} = 2$ and not any other number?
3. What is the simplified form of $\sqrt{50}$?
4. How would you approach simplifying $\sqrt{45}$?
5. Why is it helpful to remove perfect squares from under the square root?

Tip: When simplifying square roots, always look for the largest perfect square factor first to make the process easier.