The problem is about finding the length of BC in a right triangle $\triangle ABC$, where $AB = 3$, $AC = 7$, and the answer must be in simplest radical form.

We will use the Pythagorean theorem:

$AC^2 = AB^2 + BC^2$

Steps:

1. Substitute the given values: $7^2 = 3^2 + BC^2$

2. Simplify: $49 = 9 + BC^2$

3. Solve for $BC^2$: $BC^2 = 49 - 9 = 40$

4. Find $BC$ by taking the square root: $BC = \sqrt{40} = \sqrt{4 \cdot 10} = 2\sqrt{10}$

Final Answer:

$BC = 2\sqrt{10}$

The correct answer is not in the choices, so there might be an issue in the problem setup. Please confirm if you'd like further clarification or check for any inconsistencies in the data. Would you like me to revisit any steps?

Here are 5 related questions you might consider:

1. How can the Pythagorean theorem be used in different types of triangles?
2. What does it mean to simplify a square root?
3. How do you verify calculations in geometric problems like this one?
4. How can we determine if a triangle is right-angled from its side lengths?
5. What are some common errors when solving radical equations?

Tip: Always double-check square root simplifications to ensure they are fully simplified.