Simplify The Expression: $\sqrt[3]{-64} + \sqrt{64}$

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Introduction

Mathematics is a subject that deals with numbers, quantities, and shapes. It is a fundamental subject that is used in various fields such as science, engineering, economics, and finance. In mathematics, there are various operations that can be performed on numbers, such as addition, subtraction, multiplication, and division. One of the most important operations in mathematics is simplifying expressions. Simplifying expressions involves rewriting an expression in a simpler form, which can be done by combining like terms, canceling out common factors, and using mathematical properties.

Understanding the Problem

The problem we are dealing with is to simplify the expression $\sqrt[3]{-64} + \sqrt{64}$. This expression involves two types of radicals: cube root and square root. The cube root of a number is a value that, when multiplied by itself twice, gives the original number. The square root of a number is a value that, when multiplied by itself, gives the original number. In this expression, we have a cube root of -64 and a square root of 64.

Simplifying the Cube Root

To simplify the cube root of -64, we need to find a value that, when multiplied by itself twice, gives -64. We can start by finding the cube root of 64, which is 4, since $4^3 = 64$. However, we have a negative sign in front of 64, so the cube root of -64 will be -4.

Simplifying the Square Root

To simplify the square root of 64, we need to find a value that, when multiplied by itself, gives 64. We can start by finding the square root of 64, which is 8, since $8^2 = 64$.

Combining the Simplified Radicals

Now that we have simplified the cube root and the square root, we can combine them to get the final answer. We have $\sqrt[3]{-64} = -4$ and $\sqrt{64} = 8$. Therefore, the expression $\sqrt[3]{-64} + \sqrt{64}$ can be simplified to $-4 + 8$.

Final Answer

To find the final answer, we need to add -4 and 8. This gives us $-4 + 8 = 4$. Therefore, the simplified expression is $\boxed{4}$.

Conclusion

In this article, we have simplified the expression $\sqrt[3]{-64} + \sqrt{64}$. We started by understanding the problem and identifying the types of radicals involved. We then simplified the cube root and the square root separately and combined them to get the final answer. The final answer is $\boxed{4}$.

Frequently Asked Questions

• What is the cube root of -64?
• What is the square root of 64?
• How do you simplify radicals?
• What is the final answer to the expression $\sqrt[3]{-64} + \sqrt{64}$?

Step-by-Step Solution

1. Identify the types of radicals involved in the expression.
2. Simplify the cube root of -64.
3. Simplify the square root of 64.
4. Combine the simplified radicals to get the final answer.

Tips and Tricks

• When simplifying radicals, make sure to identify the type of radical involved.
• Use mathematical properties to simplify radicals.
• Combine like terms to simplify expressions.

Real-World Applications

• Simplifying radicals is an important skill in mathematics that has many real-world applications.
• It is used in various fields such as science, engineering, economics, and finance.
• Simplifying radicals can help us solve problems in a more efficient and effective way.

References

• [1] "Mathematics for Dummies" by Mark Ryan
• [2] "Algebra and Trigonometry" by Michael Sullivan
• [3] "Calculus" by Michael Spivak

Further Reading

• "Simplifying Radicals" by Math Open Reference
• "Cube Root and Square Root" by Khan Academy
• "Simplifying Expressions" by Purplemath
  

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Introduction

In our previous article, we simplified the expression $\sqrt[3]{-64} + \sqrt{64}$ and arrived at the final answer of $\boxed{4}$. However, we understand that some readers may still have questions about the problem. In this article, we will address some of the frequently asked questions (FAQs) related to the problem.

Q&A

Q: What is the cube root of -64?

A: The cube root of -64 is -4, since $(-4)^3 = -64$.

Q: What is the square root of 64?

A: The square root of 64 is 8, since $8^2 = 64$.

Q: How do you simplify radicals?

A: To simplify radicals, you need to identify the type of radical involved and then simplify it using mathematical properties. For example, to simplify the cube root of -64, you need to find a value that, when multiplied by itself twice, gives -64.

Q: What is the final answer to the expression $\sqrt[3]{-64} + \sqrt{64}$?

A: The final answer to the expression $\sqrt[3]{-64} + \sqrt{64}$ is $\boxed{4}$.

Q: Can you explain the steps to simplify the expression?

A: Yes, here are the steps to simplify the expression:

1. Identify the types of radicals involved in the expression.
2. Simplify the cube root of -64.
3. Simplify the square root of 64.
4. Combine the simplified radicals to get the final answer.

Q: What are some real-world applications of simplifying radicals?

A: Simplifying radicals has many real-world applications, including:

• Science: Simplifying radicals is used to solve problems in physics, chemistry, and biology.
• Engineering: Simplifying radicals is used to design and optimize systems, such as bridges and buildings.
• Economics: Simplifying radicals is used to model and analyze economic systems.
• Finance: Simplifying radicals is used to calculate interest rates and investment returns.

Q: Can you provide some examples of simplifying radicals?

A: Yes, here are some examples of simplifying radicals:

• $\sqrt[3]{-27} = -3$
• $\sqrt{16} = 4$
• $\sqrt[3]{64} = 4$
• $\sqrt{81} = 9$

Q: What are some common mistakes to avoid when simplifying radicals?

A: Some common mistakes to avoid when simplifying radicals include:

• Not identifying the type of radical involved.
• Not using mathematical properties to simplify radicals.
• Not combining like terms to simplify expressions.

Conclusion

In this article, we have addressed some of the frequently asked questions related to the problem of simplifying the expression $\sqrt[3]{-64} + \sqrt{64}$. We hope that this article has provided you with a better understanding of the problem and its solution.

Frequently Asked Questions

• What is the cube root of -64?
• What is the square root of 64?
• How do you simplify radicals?
• What is the final answer to the expression $\sqrt[3]{-64} + \sqrt{64}$?
• Can you explain the steps to simplify the expression?
• What are some real-world applications of simplifying radicals?
• Can you provide some examples of simplifying radicals?
• What are some common mistakes to avoid when simplifying radicals?

Step-by-Step Solution

1. Identify the types of radicals involved in the expression.
2. Simplify the cube root of -64.
3. Simplify the square root of 64.
4. Combine the simplified radicals to get the final answer.

Tips and Tricks

• When simplifying radicals, make sure to identify the type of radical involved.
• Use mathematical properties to simplify radicals.
• Combine like terms to simplify expressions.

Real-World Applications

• Simplifying radicals is an important skill in mathematics that has many real-world applications.
• It is used in various fields such as science, engineering, economics, and finance.
• Simplifying radicals can help us solve problems in a more efficient and effective way.

References

• [1] "Mathematics for Dummies" by Mark Ryan
• [2] "Algebra and Trigonometry" by Michael Sullivan
• [3] "Calculus" by Michael Spivak

Further Reading

• "Simplifying Radicals" by Math Open Reference
• "Cube Root and Square Root" by Khan Academy
• "Simplifying Expressions" by Purplemath