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To simplify the given expression into \( a + bi \) form, let's break it down step by step. The expression is:

\[
\sqrt{25} - \sqrt{-36} + \sqrt{100} - \sqrt{-49}
\]

### Step-by-step simplification:

1. **Evaluate the real square roots**:
   - \(\sqrt{25} = 5\)
   - \(\sqrt{100} = 10\)

2. **Evaluate the square roots of negative numbers** using the imaginary unit \(i\), where \( i = \sqrt{-1} \):
   - \(\sqrt{-36} = 6i\)
   - \(\sqrt{-49} = 7i\)

Now substitute the values back into the expression:

\[
5 - 6i + 10 - 7i
\]

### Combine like terms:
- Combine the real parts: \( 5 + 10 = 15 \)
- Combine the imaginary parts: \( -6i - 7i = -13i \)

Thus, the expression in \(a + bi\) form is:

\[
15 - 13i
\]

Would you like further clarification or details on any step?

### Related Questions:
1. How do you simplify square roots involving negative numbers?
2. Can you explain the concept of imaginary numbers in more depth?
3. What does \(a + bi\) form represent in complex numbers?
4. How can we visualize complex numbers on the complex plane?
5. How do operations like addition and multiplication work with complex numbers?

### Tip:
Always remember that the square root of a negative number involves the imaginary unit \(i\), where \(i^2 = -1\).

Simplify the expression to a + bi form: √25 − √−36 + √100 − √−49

Learn how to simplify square roots that involve both real and imaginary numbers. This problem demonstrates key concepts in algebra, including the use of the imaginary unit 'i' for negative square roots. Suitable for high school students in Grades 9-12.

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