https://file.aiquickdraw.com/mathbot/file/1729547860557dygr9jnw.jpg

The equation provided in the image is:

\[
p^2 = 50
\]

To solve this using the square root property, follow these steps:

1. Take the square root of both sides of the equation:

\[
p = \pm \sqrt{50}
\]

2. Simplify the square root if possible. Since \(\sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}\), we can simplify:

\[
p = \pm 5\sqrt{2}
\]

Now, the general form you are asked to fill in is:

\[
p = \pm A\sqrt{B}
\]

From the solution \(p = \pm 5\sqrt{2}\), we can see that:

\[
A = 5 \quad \text{and} \quad B = 2
\]

Thus, the values are:

- \(A = 5\)
- \(B = 2\)

Would you like further details or have any questions?

Here are 5 related questions to explore further:
1. How do we simplify square roots that involve factors like \(\sqrt{50}\)?
2. What is the square root property, and when can it be applied?
3. Why is there a \(\pm\) sign in the solution of \(p^2 = 50\)?
4. How would the solution change if the equation was \(p^2 = -50\)?
5. What are some common mistakes to avoid when simplifying radicals?

**Tip:** Always check for perfect square factors when simplifying square roots. This helps reduce the expression into its simplest form.

Solve this equation using the square root property: p^2 = 50. Find the values of A and B where the solution looks like p = ± A√B.

This problem demonstrates how to solve the equation p^2 = 50 using the square root property and simplify the result into p = ± A√B form. Learn how to express square roots and apply the square root property. Suitable for Grades 9-10.

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