What Are All The Solutions Of The Equation $p^2=\frac{9}{36}$? Show Your Work.

Introduction

Solving equations involving fractions can be a bit tricky, but with the right approach, it can be a straightforward process. In this article, we will explore the solutions of the equation $p^2=\frac{9}{36}$, and we will show our work step by step.

Simplifying the Fraction

The first step in solving this equation is to simplify the fraction on the right-hand side. We can do this by dividing both the numerator and the denominator by their greatest common divisor, which is 9.

$$\frac{9}{36} = \frac{1}{4}$$

So, the equation becomes:

$$p^2 = \frac{1}{4}$$

Taking the Square Root

To solve for $p$, we need to take the square root of both sides of the equation. This will give us two possible solutions: $p$ and $-p$.

$$p = \pm \sqrt{\frac{1}{4}}$$

Simplifying the Square Root

We can simplify the square root by finding the square root of the numerator and the denominator separately.

$$\sqrt{\frac{1}{4}} = \frac{\sqrt{1}}{\sqrt{4}} = \frac{1}{2}$$

So, the equation becomes:

$$p = \pm \frac{1}{2}$$

Solutions of the Equation

Therefore, the solutions of the equation $p^2=\frac{9}{36}$ are:

$$p = \frac{1}{2} \text{ and } p = -\frac{1}{2}$$

Conclusion

In this article, we have shown the step-by-step process of solving the equation $p^2=\frac{9}{36}$. We simplified the fraction, took the square root, and simplified the square root to find the solutions of the equation. The solutions are $p = \frac{1}{2}$ and $p = -\frac{1}{2}$.

Frequently Asked Questions

• What is the greatest common divisor of 9 and 36? The greatest common divisor of 9 and 36 is 9.
• How do you simplify a fraction? To simplify a fraction, you need to divide both the numerator and the denominator by their greatest common divisor.
• What is the square root of a fraction? The square root of a fraction is the square root of the numerator divided by the square root of the denominator.

Final Answer

The final answer is $\boxed{\frac{1}{2}, -\frac{1}{2}}$.

Introduction

In our previous article, we explored the solutions of the equation $p^2=\frac{9}{36}$. We simplified the fraction, took the square root, and simplified the square root to find the solutions of the equation. In this article, we will answer some frequently asked questions related to solving the equation $p^2=\frac{9}{36}$.

Q&A

Q: What is the greatest common divisor of 9 and 36?

A: The greatest common divisor of 9 and 36 is 9.

Q: How do you simplify a fraction?

A: To simplify a fraction, you need to divide both the numerator and the denominator by their greatest common divisor.

Q: What is the square root of a fraction?

A: The square root of a fraction is the square root of the numerator divided by the square root of the denominator.

Q: Can you explain the concept of simplifying a fraction in more detail?

A: Simplifying a fraction involves dividing both the numerator and the denominator by their greatest common divisor. This is done to reduce the fraction to its simplest form. For example, the fraction $\frac{12}{16}$ can be simplified by dividing both the numerator and the denominator by 4, resulting in $\frac{3}{4}$.

Q: How do you take the square root of a fraction?

A: To take the square root of a fraction, you need to take the square root of the numerator and the square root of the denominator separately. This is done to find the square root of the fraction. For example, the square root of $\frac{9}{36}$ is $\frac{\sqrt{9}}{\sqrt{36}} = \frac{3}{6} = \frac{1}{2}$.

Q: What is the difference between a positive and negative solution?

A: A positive solution is a value that is greater than zero, while a negative solution is a value that is less than zero. In the case of the equation $p^2=\frac{9}{36}$, the positive solution is $p = \frac{1}{2}$, while the negative solution is $p = -\frac{1}{2}$.

Q: Can you explain the concept of a negative solution in more detail?

A: A negative solution is a value that is less than zero. In the case of the equation $p^2=\frac{9}{36}$, the negative solution is $p = -\frac{1}{2}$. This means that if you were to plug in $p = -\frac{1}{2}$ into the original equation, you would get a true statement.

Q: How do you know when to use a positive or negative solution?

A: You should use a positive solution when the value is greater than zero, and a negative solution when the value is less than zero. In the case of the equation $p^2=\frac{9}{36}$, you would use the positive solution $p = \frac{1}{2}$ when the value is greater than zero, and the negative solution $p = -\frac{1}{2}$ when the value is less than zero.

Conclusion

In this article, we have answered some frequently asked questions related to solving the equation $p^2=\frac{9}{36}$. We have explained the concept of simplifying a fraction, taking the square root of a fraction, and the difference between a positive and negative solution. We hope that this article has been helpful in clarifying any confusion you may have had.

Final Answer

The final answer is $\boxed{\frac{1}{2}, -\frac{1}{2}}$.