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To find the distance between the two points \((8, 6)\) and \((3, -6)\) in simplest radical form, we can use the distance formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Where:
- \((x_1, y_1)\) = \((8, 6)\)
- \((x_2, y_2)\) = \((3, -6)\)

Substituting these values into the formula:

\[
d = \sqrt{(3 - 8)^2 + (-6 - 6)^2}
\]
\[
d = \sqrt{(-5)^2 + (-12)^2}
\]
\[
d = \sqrt{25 + 144}
\]
\[
d = \sqrt{169}
\]
\[
d = 13
\]

Thus, the distance between the two points is \( \boxed{13} \).

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:
1. How do you derive the distance formula from the Pythagorean theorem?
2. What is the distance between points \((2, 3)\) and \((-1, -4)\)?
3. How do you find the midpoint between two points?
4. Can you apply the distance formula in 3D space, and how would that change?
5. How does the distance formula apply to vectors in physics?

**Tip:** Always check that you've substituted the coordinates correctly when using the distance formula.

Find the distance between the two points (8, 6) and (3, -6) in simplest radical form.

Learn how to find the distance between two points (8, 6) and (3, -6) using the distance formula. This detailed solution walks through every step to provide the answer in simplest radical form. Suitable for students in Grades 9-12.

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