Let's break this down step by step:

You have the expression:

\[
\sqrt{(3)^2 + (-5)^2}
\]

1. First, square the numbers inside the square root:
   \[
   (3)^2 = 9 \quad \text{and} \quad (-5)^2 = 25
   \]

2. Now, add the squared values:
   \[
   9 + 25 = 34
   \]

3. Finally, take the square root of 34:
   \[
   \sqrt{34} \approx 5.83
   \]

So, \(\sqrt{(3)^2 + (-5)^2} \approx 5.83\).

Would you like more details on this solution or have any questions?

Here are 5 related questions to consider:
1. What is the geometric interpretation of \(\sqrt{(3)^2 + (-5)^2}\)?
2. How do you find the magnitude of a vector using the Pythagorean theorem?
3. How does squaring a negative number affect the result?
4. What are some applications of square roots in real-world problems?
5. How do irrational numbers, like \(\sqrt{34}\), appear in algebra?

**Tip:** Squaring a negative number always results in a positive value, since multiplying two negatives yields a positive.

Explore how to solve the expression √(3)² + (-5)² using the Pythagorean theorem. Learn step-by-step how squaring positive and negative numbers works, and how to take the square root of the sum of squares. The final answer is approximately 5.83. Suitable for Grades 7-9.

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