Select All The Correct Answers.Which Expressions Are Equivalent To The Given Expression? ( − 9 + − 4 ) − ( 2 576 + − 64 (-\sqrt{9}+\sqrt{-4})-(2 \sqrt{576}+\sqrt{-64} ( − 9 + − 4 ) − ( 2 576 + − 64 ]A. − 3 + 2 I − 2 ( 24 ) − 8 I -3+2i-2(24)-8i − 3 + 2 I − 2 ( 24 ) − 8 I B. − 3 − 2 I − 2 ( 24 ) + 8 I -3-2i-2(24)+8i − 3 − 2 I − 2 ( 24 ) + 8 I C. 45 + 10 I 45+10i 45 + 10 I D.

Mar 12, 2025 by ADMIN 384 views

Selecting the Correct Answers: Equivalent Expressions

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Understanding the Given Expression

The given expression is $(-\sqrt{9}+\sqrt{-4})-(2 \sqrt{576}+\sqrt{-64})$ . To simplify this expression, we need to evaluate the square roots and then perform the operations.

Evaluating Square Roots

$\sqrt{9}$ can be simplified as $3$ since $3^2 = 9$ .
$\sqrt{-4}$ can be simplified as $2i$ since $i^2 = -1$ and $2^2 = 4$ .
$\sqrt{576}$ can be simplified as $24$ since $24^2 = 576$ .
$\sqrt{-64}$ can be simplified as $8i$ since $i^2 = -1$ and $8^2 = 64$ .

Substituting Simplified Values

Now, we can substitute the simplified values into the given expression:

$(-\sqrt{9}+\sqrt{-4})-(2 \sqrt{576}+\sqrt{-64})$

$= (-3 + 2i) - (2(24) + 8i)$

Distributing and Combining Like Terms

Next, we need to distribute the negative sign and combine like terms:

$= -3 + 2i - 48 - 8i$

Combining Like Terms

Now, we can combine the like terms:

$= -51 - 6i$

Comparing with the Options

Comparing the simplified expression with the given options, we can see that the correct answer is:

A. $-3+2i-2(24)-8i$

However, this option is not in the correct format. Let's rewrite it in the correct format:

$-3 + 2i - 2(24) - 8i$

$= -3 + 2i - 48 - 8i$

$= -51 - 6i$

This is the same as our simplified expression. Therefore, the correct answer is:

A. $-3+2i-2(24)-8i$

Conclusion

In this article, we simplified the given expression $(-\sqrt{9}+\sqrt{-4})-(2 \sqrt{576}+\sqrt{-64})$ and compared it with the given options. We found that the correct answer is A. $-3+2i-2(24)-8i$ .

Frequently Asked Questions

What is the value of $\sqrt{9}$ $9$ ?
- The value of $\sqrt{9}$ is $3$ .
What is the value of $\sqrt{-4}$ $- 4$ ?
- The value of $\sqrt{-4}$ is $2i$ .
What is the value of $\sqrt{576}$ $576$ ?
- The value of $\sqrt{576}$ is $24$ .
What is the value of $\sqrt{-64}$ $- 64$ ?
- The value of $\sqrt{-64}$ is $8i$ .

References

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Q&A: Simplifying Expressions

Q: What is the value of $\sqrt{9}$ ?

A: The value of $\sqrt{9}$ is $3$ since $3^2 = 9$ .

Q: What is the value of $\sqrt{-4}$ ?

A: The value of $\sqrt{-4}$ is $2i$ since $i^2 = -1$ and $2^2 = 4$ .

Q: What is the value of $\sqrt{576}$ ?

A: The value of $\sqrt{576}$ is $24$ since $24^2 = 576$ .

Q: What is the value of $\sqrt{-64}$ ?

A: The value of $\sqrt{-64}$ is $8i$ since $i^2 = -1$ and $8^2 = 64$ .

Q: How do I simplify the expression $(-\sqrt{9}+\sqrt{-4})-(2 \sqrt{576}+\sqrt{-64})$ ?

A: To simplify the expression, you need to evaluate the square roots and then perform the operations. The simplified expression is $-51 - 6i$ .

Q: What is the correct answer among the options A, B, C, and D?

A: The correct answer is A. $-3+2i-2(24)-8i$ .

Q: How do I distribute and combine like terms in an expression?

A: To distribute and combine like terms, you need to follow the order of operations (PEMDAS):

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: How do I compare expressions?

A: To compare expressions, you need to simplify both expressions and then compare the simplified expressions.

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

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

Not evaluating square roots correctly
Not distributing negative signs correctly
Not combining like terms correctly
Not following the order of operations (PEMDAS)

Q: How do I practice simplifying expressions?

A: To practice simplifying expressions, you can try the following:

Start with simple expressions and gradually move on to more complex expressions.
Use online resources or math books to practice simplifying expressions.
Try simplifying expressions on your own and then check your answers with a calculator or online resources.

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

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

Calculating distances and velocities in physics
Calculating interest rates and investments in finance
Calculating probabilities and statistics in data analysis
Calculating electrical circuits and electronics in engineering

Q: How do I use technology to simplify expressions?

A: You can use technology, such as calculators or computer software, to simplify expressions. Some popular options include:

Graphing calculators
Computer algebra systems (CAS)
Online math tools and resources

Q: What are some common errors to avoid when using technology to simplify expressions?

A: Some common errors to avoid when using technology to simplify expressions include:

Not entering the expression correctly
Not selecting the correct mode or function
Not checking the answer for accuracy
Not understanding the limitations of the technology

Q: How do I choose the right technology for simplifying expressions?

A: To choose the right technology for simplifying expressions, you need to consider the following factors:

Ease of use
Accuracy
Speed
Cost
Features and functionality

Q: What are some additional resources for learning about simplifying expressions?

A: Some additional resources for learning about simplifying expressions include:

Online math tutorials and videos
Math books and textbooks
Online communities and forums
Math apps and software

Q: How do I stay motivated and engaged when learning about simplifying expressions?

A: To stay motivated and engaged when learning about simplifying expressions, you need to:

Set clear goals and objectives
Break down complex topics into smaller, manageable chunks
Practice regularly and consistently
Seek help and support when needed
Celebrate your progress and achievements