$$ \sqrt{\placeholder{}} $$$$ \sqrt{-1+2\sqrt{12}} $$

Let's simplify the expression $\sqrt{-1 + 2\sqrt{12}}$.

1. First, simplify $\sqrt{12}$:
   \[
   \sqrt{12} = \sqrt{4 \cdot 3} = 2\sqrt{3}
   \]

2. Substitute $\sqrt{12}$ back into the expression:
   \[
   \sqrt{-1 + 2\sqrt{12}} = \sqrt{-1 + 2 \cdot 2\sqrt{3}} = \sqrt{-1 + 4\sqrt{3}}
   \]

So, $\sqrt{-1 + 4\sqrt{3}}$ is the simplified form of the given expression.

Would you like more details or have any questions about this process?

Here are 5 questions you can ask:
1. How do you simplify other square root expressions?
2. Can you explain how to solve quadratic equations?
3. How do you solve systems of linear equations?
4. What are the properties of exponents and logarithms?
5. Can you explain the concept of limits in calculus?

**Tip:** Always look for perfect squares when simplifying square roots to make the process easier.

Learn how to simplify the square root of -1 plus 2 times the square root of 12 (√(-1 + 2√12)) with a step-by-step solution. This problem involves simplifying square roots and understanding the properties of radicals. Suitable for students in Grades 9-12.

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