To solve the equation \( 9p^2 - 1 = 0 \) using the square root method, follow these steps:

1. **Isolate the quadratic term**: 
   \[
   9p^2 = 1
   \]

2. **Divide both sides by 9**:
   \[
   p^2 = \frac{1}{9}
   \]

3. **Take the square root of both sides**:
   \[
   p = \pm \sqrt{\frac{1}{9}}
   \]

4. **Simplify the square root**:
   \[
   p = \pm \frac{1}{3}
   \]

So, the solutions are \( p = \frac{1}{3} \) and \( p = -\frac{1}{3} \).

Would you like further details on this solution, or do you have any questions?

Here are 5 related questions to explore:

1. How would you solve \( 4p^2 - 16 = 0 \) using the square root method?
2. What are the steps to solve \( 16x^2 - 4 = 0 \) by the square root method?
3. How would you approach solving \( 25p^2 - 36 = 0 \) using square roots?
4. Can you solve \( 9p^2 + 4 = 0 \) by the square root method? Why or why not?
5. What is the general approach for solving \( ap^2 + b = 0 \) by square roots?

**Tip:** When using the square root method, always remember to consider both the positive and negative roots when taking the square root of both sides.

Learn how to solve the quadratic equation 9p^2 - 1 = 0 using the square root method. This detailed solution covers essential algebraic concepts, including the application of square roots and the zero product property. Ideal for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation