What Is The Following Sum?$\[ 4 \sqrt{5} + 2 \sqrt{5} \\]A. $\[ 6 \sqrt{10} \\]B. $\[ 8 \sqrt{10} \\]C. $\[ 6 \sqrt{5} \\]D. $\[ 8 \sqrt{5} \\]
Understanding the Problem
The given problem involves adding two terms that contain square roots. We need to simplify the expression by combining the like terms and then determine the final result.
Breaking Down the Expression
The given expression is . To simplify this expression, we need to combine the like terms, which are the terms that contain the same square root.
Combining Like Terms
Like terms are terms that have the same variable raised to the same power. In this case, both terms contain the square root of 5. We can combine these terms by adding their coefficients.
Simplifying the Expression
To simplify the expression, we need to add the coefficients of the like terms. The coefficient of the first term is 4, and the coefficient of the second term is 2. We can add these coefficients to get the final result.
Final Result
The final result is obtained by adding the coefficients of the like terms. In this case, the final result is:
Conclusion
The final answer is . This is the result of combining the like terms in the given expression.
Why is this the Correct Answer?
The correct answer is because it is the result of adding the coefficients of the like terms. The coefficients of the like terms are 4 and 2, and their sum is 6. Therefore, the final result is .
What is the Significance of this Problem?
This problem is significant because it involves adding terms that contain square roots. This is an important concept in mathematics, and it has many real-world applications. For example, in physics, the square root of a quantity is often used to represent the magnitude of a vector.
How to Apply this Concept in Real-Life Situations
This concept can be applied in many real-life situations. For example, in physics, the square root of a quantity is often used to represent the magnitude of a vector. In engineering, the square root of a quantity is often used to represent the stress on a material.
Common Mistakes to Avoid
When adding terms that contain square roots, it is easy to make mistakes. One common mistake is to forget to combine the like terms. Another common mistake is to add the square roots instead of the coefficients.
Tips and Tricks
To avoid making mistakes when adding terms that contain square roots, it is essential to follow the order of operations. The order of operations is:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Conclusion
In conclusion, the final answer is . This is the result of combining the like terms in the given expression. The correct answer is because it is the result of adding the coefficients of the like terms. This concept is significant because it involves adding terms that contain square roots, and it has many real-world applications.
Understanding the Problem
The given problem involves adding two terms that contain square roots. We need to simplify the expression by combining the like terms and then determine the final result.
Breaking Down the Expression
The given expression is . To simplify this expression, we need to combine the like terms, which are the terms that contain the same square root.
Combining Like Terms
Like terms are terms that have the same variable raised to the same power. In this case, both terms contain the square root of 5. We can combine these terms by adding their coefficients.
Simplifying the Expression
To simplify the expression, we need to add the coefficients of the like terms. The coefficient of the first term is 4, and the coefficient of the second term is 2. We can add these coefficients to get the final result.
Final Result
The final result is obtained by adding the coefficients of the like terms. In this case, the final result is:
Conclusion
The final answer is . This is the result of combining the like terms in the given expression.
Why is this the Correct Answer?
The correct answer is because it is the result of adding the coefficients of the like terms. The coefficients of the like terms are 4 and 2, and their sum is 6. Therefore, the final result is .
What is the Significance of this Problem?
This problem is significant because it involves adding terms that contain square roots. This is an important concept in mathematics, and it has many real-world applications. For example, in physics, the square root of a quantity is often used to represent the magnitude of a vector.
How to Apply this Concept in Real-Life Situations
This concept can be applied in many real-life situations. For example, in physics, the square root of a quantity is often used to represent the magnitude of a vector. In engineering, the square root of a quantity is often used to represent the stress on a material.
Common Mistakes to Avoid
When adding terms that contain square roots, it is easy to make mistakes. One common mistake is to forget to combine the like terms. Another common mistake is to add the square roots instead of the coefficients.
Tips and Tricks
To avoid making mistakes when adding terms that contain square roots, it is essential to follow the order of operations. The order of operations is:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Conclusion
In conclusion, the final answer is . This is the result of combining the like terms in the given expression. The correct answer is because it is the result of adding the coefficients of the like terms. This concept is significant because it involves adding terms that contain square roots, and it has many real-world applications.
Understanding the Problem
The given problem involves adding two terms that contain square roots. We need to simplify the expression by combining the like terms and then determine the final result.
Breaking Down the Expression
The given expression is . To simplify this expression, we need to combine the like terms, which are the terms that contain the same square root.
Combining Like Terms
Like terms are terms that have the same variable raised to the same power. In this case, both terms contain the square root of 5. We can combine these terms by adding their coefficients.
Simplifying the Expression
To simplify the expression, we need to add the coefficients of the like terms. The coefficient of the first term is 4, and the coefficient of the second term is 2. We can add these coefficients to get the final result.
Final Result
The final result is obtained by adding the coefficients of the like terms. In this case, the final result is:
Conclusion
The final answer is . This is the result of combining the like terms in the given expression.
Why is this the Correct Answer?
The correct answer is because it is the result of adding the coefficients of the like terms. The coefficients of the like terms are 4 and 2, and their sum is 6. Therefore, the final result is .
What is the Significance of this Problem?
This problem is significant because it involves adding terms that contain square roots. This is an important concept in mathematics, and it has many real-world applications. For example, in physics, the square root of a quantity is often used to represent the magnitude of a vector.
How to Apply this Concept in Real-Life Situations
This concept can be applied in many real-life situations. For example, in physics, the square root of a quantity is often used to represent the magnitude of a vector. In engineering, the square root of a quantity is often used to represent the stress on a material.
Common Mistakes to Avoid
When adding terms that contain square roots, it is easy to make mistakes. One common mistake is to forget to combine the like terms. Another common mistake is to add the square roots instead of the coefficients.
Tips and Tricks
To avoid making mistakes when adding terms that contain square roots, it is essential to follow the order of operations. The order of operations is:
- Parentheses
Q&A: What is the Following Sum? =====================================
Q: What is the following sum?
A: The following sum is .
Q: How do I simplify the expression?
A: To simplify the expression, we need to combine the like terms, which are the terms that contain the same square root.
Q: What are like terms?
A: Like terms are terms that have the same variable raised to the same power. In this case, both terms contain the square root of 5.
Q: How do I combine like terms?
A: We can combine like terms by adding their coefficients. The coefficient of the first term is 4, and the coefficient of the second term is 2. We can add these coefficients to get the final result.
Q: What is the final result?
A: The final result is obtained by adding the coefficients of the like terms. In this case, the final result is:
Q: Why is this the correct answer?
A: The correct answer is because it is the result of adding the coefficients of the like terms. The coefficients of the like terms are 4 and 2, and their sum is 6. Therefore, the final result is .
Q: What is the significance of this problem?
A: This problem is significant because it involves adding terms that contain square roots. This is an important concept in mathematics, and it has many real-world applications. For example, in physics, the square root of a quantity is often used to represent the magnitude of a vector.
Q: How can I apply this concept in real-life situations?
A: This concept can be applied in many real-life situations. For example, in physics, the square root of a quantity is often used to represent the magnitude of a vector. In engineering, the square root of a quantity is often used to represent the stress on a material.
Q: What are some common mistakes to avoid when adding terms that contain square roots?
A: When adding terms that contain square roots, it is easy to make mistakes. One common mistake is to forget to combine the like terms. Another common mistake is to add the square roots instead of the coefficients.
Q: How can I avoid making mistakes when adding terms that contain square roots?
A: To avoid making mistakes when adding terms that contain square roots, it is essential to follow the order of operations. The order of operations is:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: What is the final answer?
A: The final answer is .
Q: Why is this the correct answer?
A: The correct answer is because it is the result of adding the coefficients of the like terms. The coefficients of the like terms are 4 and 2, and their sum is 6. Therefore, the final result is .
Conclusion
In conclusion, the final answer is . This is the result of combining the like terms in the given expression. The correct answer is because it is the result of adding the coefficients of the like terms. This concept is significant because it involves adding terms that contain square roots, and it has many real-world applications.