Which of these expressions is equivalent to 𝟐+√−𝟑𝟔 ? 

The expression given is \(2 + \sqrt{-36}\). To find an equivalent expression, let's first simplify \(\sqrt{-36}\).

### Step-by-step Solution:

1. **Simplify the square root of a negative number:**

   \[
   \sqrt{-36} = \sqrt{-1 \cdot 36} = \sqrt{-1} \cdot \sqrt{36}
   \]

2. **Recognize that \(\sqrt{-1}\) is defined as \(i\) (the imaginary unit):**

   \[
   \sqrt{-1} = i
   \]

3. **Simplify \(\sqrt{36}\):**

   \[
   \sqrt{36} = 6
   \]

4. **Combine the terms:**

   \[
   \sqrt{-36} = 6i
   \]

5. **Substitute back into the original expression:**

   \[
   2 + \sqrt{-36} = 2 + 6i
   \]

So, the equivalent expression to \(2 + \sqrt{-36}\) is **\(2 + 6i\)**.

Would you like a more detailed explanation or have any questions? Here are some related questions that you might find useful:

1. What is the imaginary unit \(i\) and how is it used in complex numbers?
2. How do you add and subtract complex numbers?
3. What is the significance of the square root of negative numbers in mathematics?
4. How can you graph complex numbers on a complex plane?
5. What is the difference between real numbers and complex numbers?

**Tip:** When dealing with square roots of negative numbers, always remember that \(\sqrt{-1} = i\).

Which of these expressions is equivalent to 𝟐+√−𝟑𝟔?

Explore how to simplify the expression 2 + √−36 using imaginary numbers. This solution walks you through step-by-step by recognizing √−1 as the imaginary unit 'i' and simplifying the square root of negative numbers. Perfect for students in Grades 9-12 learning about complex numbers and square roots of negative values.

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