Evaluate The Expression For Z = − 8.7 Z = -8.7 Z = − 8.7 . Z 2 Z^2 Z 2 Calculate Z 2 Z^2 Z 2 .

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Introduction

In mathematics, evaluating expressions is a fundamental concept that involves substituting values into mathematical expressions to obtain a result. In this article, we will focus on evaluating the expression $z^2$ for a given value of $z$. We will use the value $z = -8.7$ to calculate $z^2$.

Understanding the Expression

The expression $z^2$ represents the square of the variable $z$. To calculate $z^2$, we need to multiply the value of $z$ by itself. In other words, $z^2 = z \times z$.

Substituting the Value of $z$

We are given the value of $z$ as $-8.7$. To calculate $z^2$, we need to substitute this value into the expression $z^2$. This means we need to multiply $-8.7$ by itself.

Calculating $z^2$

To calculate $z^2$, we can use the formula $z^2 = z \times z$. Substituting the value of $z$ as $-8.7$, we get:

$z^2 = -8.7 \times -8.7$

Using the Order of Operations

When multiplying two negative numbers, we need to follow the order of operations. The order of operations states that we need to perform multiplication before addition or subtraction. In this case, we need to multiply $-8.7$ by $-8.7$.

Performing the Multiplication

To perform the multiplication, we can use the following steps:

1. Multiply the absolute values of the two numbers: $8.7 \times 8.7 = 75.69$
2. Determine the sign of the result: Since both numbers are negative, the result will be positive.

Calculating the Final Result

Using the steps above, we can calculate the final result:

$z^2 = 75.69$

Conclusion

In this article, we evaluated the expression $z^2$ for a given value of $z$. We used the value $z = -8.7$ to calculate $z^2$. By following the order of operations and performing the multiplication, we obtained the final result of $z^2 = 75.69$.

Frequently Asked Questions

• What is the expression $z^2$? The expression $z^2$ represents the square of the variable $z$.
• How do we calculate $z^2$? To calculate $z^2$, we need to multiply the value of $z$ by itself.
• What is the order of operations? The order of operations states that we need to perform multiplication before addition or subtraction.
• How do we determine the sign of the result when multiplying two negative numbers? Since both numbers are negative, the result will be positive.

Further Reading

• Evaluating Expressions: A Comprehensive Guide
• Understanding the Order of Operations
• Calculating Squares and Square Roots

References

• [1] "Evaluating Expressions" by Math Open Reference
• [2] "Order of Operations" by Khan Academy
• [3] "Calculating Squares and Square Roots" by Mathway
  

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Introduction

In our previous article, we evaluated the expression $z^2$ for a given value of $z$. We used the value $z = -8.7$ to calculate $z^2$. In this article, we will answer some frequently asked questions related to evaluating expressions, particularly for the expression $z^2$.

Q&A

Q: What is the expression $z^2$?

A: The expression $z^2$ represents the square of the variable $z$. It is calculated by multiplying the value of $z$ by itself.

Q: How do we calculate $z^2$?

A: To calculate $z^2$, we need to multiply the value of $z$ by itself. This can be done using the formula $z^2 = z \times z$.

Q: What is the order of operations?

A: The order of operations states that we need to perform multiplication before addition or subtraction. This means that when we have multiple operations in an expression, we need to perform the operations in the following order:

1. Parentheses
2. Exponents (such as squaring or cubing)
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)

Q: How do we determine the sign of the result when multiplying two negative numbers?

A: When multiplying two negative numbers, the result is always positive. This is because the negative signs cancel each other out.

Q: What is the difference between $z^2$ and $z \times z$?

A: $z^2$ and $z \times z$ are equivalent expressions. They both represent the square of the variable $z$. The difference is that $z^2$ is a more concise way of writing the expression, while $z \times z$ is a more explicit way of writing it.

Q: Can we use a calculator to calculate $z^2$?

A: Yes, we can use a calculator to calculate $z^2$. Simply enter the value of $z$ into the calculator and press the "square" button to calculate the result.

Q: What if we have a decimal value for $z$?

A: If we have a decimal value for $z$, we can still calculate $z^2$ using a calculator. Simply enter the decimal value of $z$ into the calculator and press the "square" button to calculate the result.

Q: Can we use a spreadsheet to calculate $z^2$?

A: Yes, we can use a spreadsheet to calculate $z^2$. Simply enter the value of $z$ into a cell in the spreadsheet and use a formula to calculate the result.

Conclusion

In this article, we answered some frequently asked questions related to evaluating expressions, particularly for the expression $z^2$. We covered topics such as the order of operations, determining the sign of the result when multiplying two negative numbers, and using calculators and spreadsheets to calculate $z^2$.

Frequently Asked Questions

• What is the expression $z^2$?
• How do we calculate $z^2$?
• What is the order of operations?
• How do we determine the sign of the result when multiplying two negative numbers?
• What is the difference between $z^2$ and $z \times z$?
• Can we use a calculator to calculate $z^2$?
• What if we have a decimal value for $z$?
• Can we use a spreadsheet to calculate $z^2$?

Further Reading

• Evaluating Expressions: A Comprehensive Guide
• Understanding the Order of Operations
• Calculating Squares and Square Roots

References

• [1] "Evaluating Expressions" by Math Open Reference
• [2] "Order of Operations" by Khan Academy
• [3] "Calculating Squares and Square Roots" by Mathway