Simplify: $\sqrt[3]{1}$A. $\frac{1}{3}$ B. 1 C. 9 D. 3

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Understanding the Concept of Cube Root

The cube root of a number is a value that, when multiplied by itself twice, gives the original number. In mathematical terms, it is represented as $\sqrt[3]{x}$, where $x$ is the number inside the cube root symbol. In this case, we are dealing with the cube root of 1, denoted as $\sqrt[3]{1}$.

Evaluating the Cube Root of 1

To simplify $\sqrt[3]{1}$, we need to find a value that, when multiplied by itself twice, equals 1. Since 1 multiplied by itself any number of times will always result in 1, the cube root of 1 is simply 1.

Analyzing the Options

Now, let's analyze the given options:

A. $\frac{1}{3}$: This is the cube root of 1, but it is not the correct answer because it is not equal to 1.

B. 1: This is the correct answer because 1 multiplied by itself twice equals 1.

C. 9: This is not the correct answer because 9 is not equal to 1.

D. 3: This is not the correct answer because 3 is not equal to 1.

Conclusion

In conclusion, the cube root of 1 is simply 1. This is because 1 multiplied by itself twice equals 1, making it the correct answer.

Frequently Asked Questions

• What is the cube root of 1?
• How do you simplify the cube root of 1?
• What is the value of $\sqrt[3]{1}$?

Answering the FAQs

• The cube root of 1 is 1.
• To simplify the cube root of 1, you need to find a value that, when multiplied by itself twice, equals 1.
• The value of $\sqrt[3]{1}$ is 1.

Real-World Applications

The concept of cube root is used in various real-world applications, such as:

• Calculating volumes of cubes
• Determining the length of the sides of a cube
• Finding the surface area of a cube

Example Problems

• Find the cube root of 27.
• Simplify $\sqrt[3]{64}$.
• Calculate the volume of a cube with a side length of 5.

Solutions to Example Problems

• The cube root of 27 is 3.
• $\sqrt[3]{64}$ simplifies to 4.
• The volume of a cube with a side length of 5 is 125.

Conclusion

In conclusion, the cube root of 1 is simply 1. This is because 1 multiplied by itself twice equals 1, making it the correct answer. The concept of cube root is used in various real-world applications, and it is essential to understand how to simplify cube roots to solve problems in mathematics and other fields.

Final Thoughts

The cube root of 1 is a fundamental concept in mathematics that is used to calculate volumes, determine the length of the sides of a cube, and find the surface area of a cube. By understanding how to simplify cube roots, you can solve problems in mathematics and other fields with ease.

References

• [1] Khan Academy. (n.d.). Cube Root. Retrieved from https://www.khanacademy.org/math/algebra/x2f1f4f/x2f1f4f-cube-root
• [2] Math Open Reference. (n.d.). Cube Root. Retrieved from https://www.mathopenref.com/cuberoot.html
• [3] Wolfram MathWorld. (n.d.). Cube Root. Retrieved from https://mathworld.wolfram.com/CubeRoot.html

Keywords

• Cube root
• Simplify
• $\sqrt[3]{1}$
• 1
• Mathematics
• Real-world applications
• Example problems
• Solutions
• References
  

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Frequently Asked Questions

We have received many questions about the cube root of 1, and we are happy to provide answers to some of the most frequently asked questions.

Q: What is the cube root of 1?

A: The cube root of 1 is 1.

Q: How do you simplify the cube root of 1?

A: To simplify the cube root of 1, you need to find a value that, when multiplied by itself twice, equals 1.

Q: What is the value of $\sqrt[3]{1}$?

A: The value of $\sqrt[3]{1}$ is 1.

Q: Can you provide an example of how to simplify the cube root of 1?

A: Yes, here is an example:

$\sqrt[3]{1} = 1$

Q: How do you calculate the cube root of a number?

A: To calculate the cube root of a number, you need to find a value that, when multiplied by itself twice, equals the original number.

Q: Can you provide a real-world application of the cube root of 1?

A: Yes, here is an example:

• Calculating the volume of a cube with a side length of 1.

Q: How do you determine the length of the sides of a cube?

A: To determine the length of the sides of a cube, you need to calculate the cube root of the volume of the cube.

Q: Can you provide a solution to the problem of finding the cube root of 27?

A: Yes, here is the solution:

$\sqrt[3]{27} = 3$

Q: How do you simplify the cube root of 64?

A: To simplify the cube root of 64, you need to find a value that, when multiplied by itself twice, equals 64.

Q: Can you provide a reference for the cube root of 1?

A: Yes, here are some references:

• [1] Khan Academy. (n.d.). Cube Root. Retrieved from https://www.khanacademy.org/math/algebra/x2f1f4f/x2f1f4f-cube-root
• [2] Math Open Reference. (n.d.). Cube Root. Retrieved from https://www.mathopenref.com/cuberoot.html
• [3] Wolfram MathWorld. (n.d.). Cube Root. Retrieved from https://mathworld.wolfram.com/CubeRoot.html

Additional Resources

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Related Articles

• Cube Root: A Comprehensive Guide
• Simplifying Cube Roots: Tips and Tricks
• Real-World Applications of Cube Roots

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Keywords

• Cube root
• Simplify
• $\sqrt[3]{1}$
• 1
• Mathematics
• Real-world applications
• Example problems
• Solutions
• References
• Q&A
• Frequently asked questions