Select The Correct Answer.What Is The Simplified Form Of $3 \sqrt{7} - 5 \sqrt{7}$?A. $-2 \sqrt{7}$ B. \$2 \sqrt{7}$[/tex\] C. $-\sqrt{14}$ D. $15 \sqrt{7}$
Understanding the Basics of Radical Expressions
Radical expressions are mathematical expressions that involve the use of square roots, cube roots, and other roots. In this article, we will focus on simplifying radical expressions, specifically the expression $3 \sqrt{7} - 5 \sqrt{7}$.
What is a Simplified Radical Expression?
A simplified radical expression is a radical expression that has been reduced to its simplest form. This means that the expression has been simplified by removing any unnecessary or redundant terms.
The Expression $3 \sqrt{7} - 5 \sqrt{7}$
The expression $3 \sqrt{7} - 5 \sqrt{7}$ is a radical expression that involves the subtraction of two terms. To simplify this expression, we need to combine the two terms by subtracting their coefficients.
Combining Like Terms
Like terms are terms that have the same variable and exponent. In this case, the two terms $3 \sqrt{7}$ and $-5 \sqrt{7}$ are like terms because they both have the same variable $\sqrt{7}$ and the same exponent (which is 1).
Simplifying the Expression
To simplify the expression $3 \sqrt{7} - 5 \sqrt{7}$, we need to combine the two terms by subtracting their coefficients. This can be done by subtracting the coefficient of the second term from the coefficient of the first term.
Evaluating the Expression
Now that we have combined the two terms, we can evaluate the expression by simplifying the coefficient.
Conclusion
In conclusion, the simplified form of the expression $3 \sqrt{7} - 5 \sqrt{7}$ is $-2 \sqrt{7}$. This is because we combined the two like terms by subtracting their coefficients and then evaluated the expression by simplifying the coefficient.
Answer Key
The correct answer is:
- A. $-2 \sqrt{7}$
Why is this the Correct Answer?
This is the correct answer because we simplified the expression by combining the two like terms and then evaluating the expression by simplifying the coefficient. The other options are incorrect because they do not accurately represent the simplified form of the expression.
Common Mistakes to Avoid
When simplifying radical expressions, it is easy to make mistakes. Here are some common mistakes to avoid:
- Not combining like terms
- Not evaluating the expression after combining like terms
- Not simplifying the coefficient
Tips for Simplifying Radical Expressions
Here are some tips for simplifying radical expressions:
- Combine like terms by adding or subtracting their coefficients
- Evaluate the expression after combining like terms
- Simplify the coefficient by combining any like terms
Conclusion
In conclusion, simplifying radical expressions is an important skill in mathematics. By following the steps outlined in this article, you can simplify radical expressions with ease. Remember to combine like terms, evaluate the expression, and simplify the coefficient to get the correct answer.
Final Answer
The final answer is:
- A. $-2 \sqrt{7}$
Simplifying Radical Expressions: A Q&A Guide =====================================================
Frequently Asked Questions
In this article, we will answer some of the most frequently asked questions about simplifying radical expressions.
Q: What is a radical expression?
A: A radical expression is a mathematical expression that involves the use of square roots, cube roots, and other roots.
Q: What is the difference between a simplified radical expression and a non-simplified radical expression?
A: A simplified radical expression is a radical expression that has been reduced to its simplest form, while a non-simplified radical expression is a radical expression that has not been reduced to its simplest form.
Q: How do I simplify a radical expression?
A: To simplify a radical expression, you need to combine like terms by adding or subtracting their coefficients, evaluate the expression after combining like terms, and simplify the coefficient by combining any like terms.
Q: What are like terms in a radical expression?
A: Like terms in a radical expression are terms that have the same variable and exponent.
Q: How do I combine like terms in a radical expression?
A: To combine like terms in a radical expression, you need to add or subtract their coefficients.
Q: What is the coefficient of a radical expression?
A: The coefficient of a radical expression is the number that is multiplied by the variable.
Q: How do I simplify the coefficient of a radical expression?
A: To simplify the coefficient of a radical expression, you need to combine any like terms.
Q: What is the final answer to the expression $3 \sqrt{7} - 5 \sqrt{7}$?
A: The final answer to the expression $3 \sqrt{7} - 5 \sqrt{7}$ is $-2 \sqrt{7}$.
Q: Why is the final answer $-2 \sqrt{7}$ and not $2 \sqrt{7}$?
A: The final answer is $-2 \sqrt{7}$ because the expression $3 \sqrt{7} - 5 \sqrt{7}$ involves the subtraction of two terms, and when you subtract the coefficients, you get $-2$.
Q: Can I simplify a radical expression with a variable?
A: Yes, you can simplify a radical expression with a variable. However, you need to follow the same steps as before: combine like terms, evaluate the expression, and simplify the coefficient.
Q: What are some common mistakes to avoid when simplifying radical expressions?
A: Some common mistakes to avoid when simplifying radical expressions include not combining like terms, not evaluating the expression after combining like terms, and not simplifying the coefficient.
Q: How can I practice simplifying radical expressions?
A: You can practice simplifying radical expressions by working through examples and exercises. You can also use online resources and practice tests to help you improve your skills.
Conclusion
In conclusion, simplifying radical expressions is an important skill in mathematics. By following the steps outlined in this article and practicing regularly, you can become proficient in simplifying radical expressions.
Final Answer
The final answer is:
- A. $-2 \sqrt{7}$