Which Of These Numbers Are Solutions Of $n^2=36$? Choose TWO Correct Answers.A. -18 B. $-9$ C. $-6$ D. 6 E. 9 F. 18

Introduction

When solving equations involving squares, it's essential to consider both positive and negative solutions. In this case, we're looking for numbers that satisfy the equation $n^2=36$. To find these solutions, we need to consider the square root of 36 and its negative counterpart.

Understanding the Equation

The equation $n^2=36$ can be rewritten as $n^2-36=0$. This is a quadratic equation that can be factored as $(n-6)(n+6)=0$. By setting each factor equal to zero, we can find the solutions for $n$.

Finding the Solutions

To find the solutions, we set each factor equal to zero and solve for $n$.

• For the factor $n-6=0$, we add 6 to both sides to get $n=6$.
• For the factor $n+6=0$, we subtract 6 from both sides to get $n=-6$.

Considering the Options

Now that we have the solutions $n=6$ and $n=-6$, we can compare them to the options provided.

• Option A is $-18$, which is not a solution to the equation.
• Option B is $-9$, which is not a solution to the equation.
• Option C is $-6$, which is a solution to the equation.
• Option D is $6$, which is a solution to the equation.
• Option E is $9$, which is not a solution to the equation.
• Option F is $18$, which is not a solution to the equation.

Conclusion

Based on our analysis, the two correct answers are C. $-6$ and D. 6. These are the only two options that satisfy the equation $n^2=36$.

Additional Considerations

It's worth noting that the negative solution $n=-6$ is often overlooked in favor of the positive solution $n=6$. However, both solutions are valid and should be considered when solving equations involving squares.

Final Thoughts

When solving equations involving squares, it's essential to consider both positive and negative solutions. By doing so, we can ensure that we find all possible solutions and avoid missing any valid answers. In this case, the two correct answers are C. $-6$ and D. 6.

Introduction

In our previous article, we discussed the solutions to the equation $n^2=36$. We found that the two correct answers are C. $-6$ and D. 6. However, we understand that you may still have some questions about this topic. In this article, we'll address some of the most frequently asked questions (FAQs) about solutions to $n^2=36$.

Q: What is the equation $n^2=36$?

A: The equation $n^2=36$ is a quadratic equation that can be rewritten as $n^2-36=0$. This equation is asking for a number $n$ that, when squared, equals 36.

Q: How do I find the solutions to $n^2=36$?

A: To find the solutions, you can factor the equation as $(n-6)(n+6)=0$. Then, set each factor equal to zero and solve for $n$. This will give you the solutions $n=6$ and $n=-6$.

Q: Why are there two solutions to $n^2=36$?

A: There are two solutions to $n^2=36$ because the square of a negative number is positive. In this case, the negative solution $n=-6$ is a valid solution because $(-6)^2=36$.

Q: Can I use a calculator to find the solutions to $n^2=36$?

A: Yes, you can use a calculator to find the solutions to $n^2=36$. Simply enter the equation $n^2=36$ into your calculator and press the "solve" button. Your calculator will give you the solutions $n=6$ and $n=-6$.

Q: What if I only want to find the positive solution to $n^2=36$?

A: If you only want to find the positive solution to $n^2=36$, you can simply ignore the negative solution $n=-6$. However, keep in mind that the negative solution is also a valid solution.

Q: Can I use the equation $n^2=36$ to find other solutions?

A: Yes, you can use the equation $n^2=36$ to find other solutions. For example, if you want to find the solutions to $n^2=144$, you can simply multiply both sides of the equation by 4 to get $n^2=144$. Then, factor the equation as $(n-12)(n+12)=0$ and solve for $n$.

Q: What if I'm still having trouble finding the solutions to $n^2=36$?

A: If you're still having trouble finding the solutions to $n^2=36$, try using a different method, such as graphing the equation on a coordinate plane. You can also try using a calculator or online tool to help you find the solutions.

Conclusion

We hope this article has helped to answer some of your questions about solutions to $n^2=36$. Remember, the two correct answers are C. $-6$ and D. 6. If you have any more questions or need further clarification, feel free to ask.

Additional Resources

If you're looking for more information about solutions to quadratic equations, we recommend checking out the following resources:

• Khan Academy: Quadratic Equations
• Mathway: Quadratic Equations
• Wolfram Alpha: Quadratic Equations

We hope these resources are helpful in your studies.