Perform the operation and write the result in standard form. (Simplify your answer completely.)

−2 + root-8) + (7 - root-50)

To simplify the expression \(-2 + \sqrt{-8} + 7 - \sqrt{-50}\), let's break it down step-by-step. 

### Step 1: Handle imaginary components.
Recall that \(\sqrt{-a} = i\sqrt{a}\), where \(i\) is the imaginary unit.

- \(\sqrt{-8} = i\sqrt{8} = i \cdot 2\sqrt{2}\)
- \(\sqrt{-50} = i\sqrt{50} = i \cdot 5\sqrt{2}\)

Thus, the expression becomes:
\[
(-2 + 7) + (i \cdot 2\sqrt{2} - i \cdot 5\sqrt{2})
\]

### Step 2: Simplify the real and imaginary parts separately.
- Real part: \(-2 + 7 = 5\)
- Imaginary part: \(i \cdot 2\sqrt{2} - i \cdot 5\sqrt{2} = -3i\sqrt{2}\)

### Step 3: Write the result in standard form.
The standard form of a complex number is \(a + bi\), where \(a\) and \(b\) are real numbers.

Thus, the result is:
\[
5 - 3i\sqrt{2}
\]

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Would you like more details or have any questions?

Here are five related questions for further exploration:
1. How do you simplify other complex expressions involving roots?
2. What are the properties of the imaginary unit \(i\)?
3. How do you multiply two complex numbers?
4. How do you convert complex numbers to polar form?
5. How can complex roots be visualized on the complex plane?

**Tip:** Remember, when working with roots of negative numbers, always separate the imaginary unit \(i\) to avoid mistakes.

Perform the operation and write the result in standard form. (Simplify your answer completely.) −2 + root-8) + (7 - root-50)

Learn how to simplify the expression −2 + √-8 + 7 − √-50. This problem involves complex numbers, the imaginary unit, and square roots of negative numbers. Suitable for high school students studying Grades 10-12 mathematics.

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