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We are given the equation \( p^2 = 0.81 \).

### Step-by-step solution:
1. To find \( p \), take the square root of both sides of the equation:
   \[
   p = \pm \sqrt{0.81}
   \]

2. The square root of \( 0.81 \) is:
   \[
   \sqrt{0.81} = 0.9
   \]

   Therefore, the possible values of \( p \) are:
   \[
   p = 0.9 \quad \text{or} \quad p = -0.9
   \]

### Now let's check the provided answer options:
- **Option A**: \( p = \sqrt{0.81} \) — this is correct because \( \sqrt{0.81} = 0.9 \).
- **Option B**: \( p = -\sqrt{0.81} \) — this is also correct because \( -\sqrt{0.81} = -0.9 \).
- **Option C**: \( p = 0.9 \) — correct, as \( 0.9 \) is one of the solutions.
- **Option D**: \( p = -0.9 \) — correct, as \( -0.9 \) is also one of the solutions.
- **Option E**: None of the above — incorrect, since both \( 0.9 \) and \( -0.9 \) are valid solutions.

### Correct answers: A, B, C, and D.

Would you like further explanation or details on this? Here are some related questions:

1. How do we handle square roots of negative numbers?
2. What is the general method for solving quadratic equations?
3. How do we know when to include both positive and negative solutions?
4. What is the significance of the square root in real and complex numbers?
5. Can there be more than two solutions for a quadratic equation?

**Tip**: Remember that when you solve equations like \( x^2 = a \), always consider both the positive and negative square roots of \( a \).

Which of the p values are solutions to the following equation? p^2 = 0.81. Choose all answers that apply: A) p = sqrt(0.81), B) p = -sqrt(0.81), C) p = 0.9, D) p = -0.9, E) None of the above.

Explore the solution to the quadratic equation p^2 = 0.81 by finding both the positive and negative square roots. This problem covers key concepts in quadratic equations and algebra, suitable for Grades 7-9.

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