Evaluate: ( 111.2 ) 2 = (\sqrt{111.2})^2 = ( 111.2 ​ ) 2 =

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Introduction

Understanding the Problem In mathematics, we often encounter problems that involve the manipulation of numbers and mathematical operations. One such problem is the evaluation of the expression $(\sqrt{111.2})^2$. This problem requires us to apply our knowledge of square roots and exponentiation to arrive at the correct solution.

The Square Root Function

The square root function, denoted by $\sqrt{x}$, is a mathematical operation that returns the value of a number that, when multiplied by itself, gives the original number. In other words, if $y = \sqrt{x}$, then $y^2 = x$. This function is used to find the value of a number that, when squared, gives a specified value.

Evaluating the Expression

To evaluate the expression $(\sqrt{111.2})^2$, we need to follow the order of operations (PEMDAS):

1. Evaluate the expression inside the square root: $\sqrt{111.2}$
2. Raise the result to the power of 2

Step 1: Evaluate the Expression Inside the Square Root

To evaluate the expression inside the square root, we need to find the value of $\sqrt{111.2}$. This can be done using a calculator or by approximating the value using a table of square roots.

Approximating the Value Using a table of square roots, we can approximate the value of $\sqrt{111.2}$ as follows:

$\sqrt{111.2} \approx 10.5$

Step 2: Raise the Result to the Power of 2

Now that we have the value of $\sqrt{111.2}$, we can raise it to the power of 2 to get the final result.

$(\sqrt{111.2})^2 = (10.5)^2$

Calculating the Final Result

To calculate the final result, we need to multiply 10.5 by itself.

$(10.5)^2 = 110.25$

Conclusion

In conclusion, the value of the expression $(\sqrt{111.2})^2$ is 110.25. This problem required us to apply our knowledge of square roots and exponentiation to arrive at the correct solution.

Importance of Understanding Square Roots

Understanding square roots is crucial in mathematics and has numerous applications in real-life situations. For example, in physics, square roots are used to calculate the velocity of an object, while in engineering, they are used to calculate the stress on a material.

Real-World Applications of Square Roots

Square roots have numerous real-world applications, including:

• Calculating the area of a circle
• Determining the length of a diagonal in a rectangle
• Finding the height of a triangle
• Calculating the velocity of an object

Tips for Evaluating Expressions with Square Roots

When evaluating expressions with square roots, it's essential to follow the order of operations (PEMDAS) and to approximate the value of the square root using a table or calculator.

Common Mistakes to Avoid

When evaluating expressions with square roots, some common mistakes to avoid include:

• Forgetting to follow the order of operations (PEMDAS)
• Approximating the value of the square root incorrectly
• Not raising the result to the power of 2

Final Thoughts

In conclusion, evaluating the expression $(\sqrt{111.2})^2$ requires us to apply our knowledge of square roots and exponentiation. By following the order of operations (PEMDAS) and approximating the value of the square root using a table or calculator, we can arrive at the correct solution. Understanding square roots is crucial in mathematics and has numerous applications in real-life situations.

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Introduction

In our previous article, we evaluated the expression $(\sqrt{111.2})^2$ and arrived at the correct solution. However, we understand that some readers may still have questions or doubts about the problem. In this article, we will address some of the most frequently asked questions about the expression $(\sqrt{111.2})^2$.

Q&A

Q: What is the square root function?

A: The square root function, denoted by $\sqrt{x}$, is a mathematical operation that returns the value of a number that, when multiplied by itself, gives the original number. In other words, if $y = \sqrt{x}$, then $y^2 = x$.

Q: How do I evaluate the expression $(\sqrt{111.2})^2$?

A: To evaluate the expression $(\sqrt{111.2})^2$, you need to follow the order of operations (PEMDAS):

1. Evaluate the expression inside the square root: $\sqrt{111.2}$
2. Raise the result to the power of 2

Q: What is the value of $\sqrt{111.2}$?

A: The value of $\sqrt{111.2}$ is approximately 10.5.

Q: Why do I need to raise the result to the power of 2?

A: You need to raise the result to the power of 2 because the expression $(\sqrt{111.2})^2$ is asking for the square of the square root of 111.2.

Q: Can I use a calculator to evaluate the expression $(\sqrt{111.2})^2$?

A: Yes, you can use a calculator to evaluate the expression $(\sqrt{111.2})^2$. However, it's also important to understand the mathematical concept behind the problem.

Q: What are some real-world applications of square roots?

A: Square roots have numerous real-world applications, including:

• Calculating the area of a circle
• Determining the length of a diagonal in a rectangle
• Finding the height of a triangle
• Calculating the velocity of an object

Q: What are some common mistakes to avoid when evaluating expressions with square roots?

A: Some common mistakes to avoid when evaluating expressions with square roots include:

• Forgetting to follow the order of operations (PEMDAS)
• Approximating the value of the square root incorrectly
• Not raising the result to the power of 2

Conclusion

In conclusion, evaluating the expression $(\sqrt{111.2})^2$ requires us to apply our knowledge of square roots and exponentiation. By following the order of operations (PEMDAS) and approximating the value of the square root using a table or calculator, we can arrive at the correct solution. We hope that this Q&A article has helped to clarify any doubts or questions you may have had about the problem.

Additional Resources

If you have any further questions or need additional help with evaluating expressions with square roots, we recommend the following resources:

• Khan Academy: Square Roots
• Mathway: Square Roots
• Wolfram Alpha: Square Roots

Final Thoughts

In conclusion, understanding square roots is crucial in mathematics and has numerous applications in real-life situations. By following the order of operations (PEMDAS) and approximating the value of the square root using a table or calculator, we can arrive at the correct solution. We hope that this Q&A article has helped to clarify any doubts or questions you may have had about the problem.