The Area Of A Square Piece Of Land In Square Units Can Be Represented By The Expression 9 Q 4 R 6 S 6 9q^4r^6s^6 9 Q 4 R 6 S 6 . What Is The Length Of One Side Of The Piece Of Land?A. 3 Q 2 R 6 ∣ S 3 ∣ 3q^2r^6|s^3| 3 Q 2 R 6 ∣ S 3 ∣ Units B. 3 Q 2 R 4 ∣ S 3 ∣ 3q^2r^4|s^3| 3 Q 2 R 4 ∣ S 3 ∣ Units C.

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Introduction

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When it comes to calculating the area of a square piece of land, we often rely on the formula: Area = side^2. However, in this scenario, the area is represented by the expression $9q^4r^6s^6$. Our goal is to find the length of one side of the piece of land, which is a crucial piece of information for various applications, such as real estate, architecture, and engineering.

Understanding the Expression

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The given expression $9q^4r^6s^6$ represents the area of the square piece of land. To find the length of one side, we need to take the square root of the area. However, before we do that, let's break down the expression and understand its components.

• The expression consists of three variables: q, r, and s.
• Each variable is raised to a power: q^4, r^6, and s^6.
• The expression is multiplied by 9, which is a constant.

Finding the Length of One Side

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To find the length of one side, we need to take the square root of the area. However, we cannot simply take the square root of the entire expression. Instead, we need to take the square root of each variable and then multiply the results.

Let's start by taking the square root of the constant 9:

$$\sqrt{9} = 3$$

Next, we need to take the square root of each variable:

$$\sqrt{q^4} = q^2$$

$$\sqrt{r^6} = r^3$$

$$\sqrt{s^6} = s^3$$

Now, we can multiply the results:

$$3q^2r^3s^3$$

However, we are not done yet. We need to consider the absolute value of each variable. This is because the length of a side cannot be negative.

$$3q^2r^3|s^3|$$

Conclusion

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In conclusion, the length of one side of the square piece of land is $3q^2r^3|s^3|$ units. This is the correct answer, and it is based on the given expression $9q^4r^6s^6$.

Comparison with Other Options

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Let's compare our answer with the other options:

• Option A: $3q^2r^6|s^3|$ units
• Option B: $3q^2r^4|s^3|$ units
• Option C: (not provided)

Our answer is different from option A, which has $r^6$ instead of $r^3$. Our answer is also different from option B, which has $r^4$ instead of $r^3$.

Final Thoughts

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In conclusion, the length of one side of the square piece of land is $3q^2r^3|s^3|$ units. This is the correct answer, and it is based on the given expression $9q^4r^6s^6$. We hope this article has provided valuable insights into the calculation of the length of one side of a square piece of land.

References

• [1] Algebraic expressions and equations
• [2] Square roots and absolute values
• [3] Calculating the length of one side of a square piece of land

Related Articles

• [Calculating the Area of a Square Piece of Land](link to article)
• [Understanding Algebraic Expressions and Equations](link to article)
• [Square Roots and Absolute Values: A Comprehensive Guide](link to article)
  

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Introduction

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In our previous article, we discussed how to find the length of one side of a square piece of land given the expression $9q^4r^6s^6$. We also compared our answer with other options and provided a comprehensive guide to understanding algebraic expressions and equations, square roots, and absolute values.

In this article, we will provide a Q&A section to address any questions or concerns you may have regarding the calculation of the length of one side of a square piece of land.

Q&A

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Q: What is the formula for finding the length of one side of a square piece of land?

A: The formula for finding the length of one side of a square piece of land is:

$$\text{Length} = \sqrt{\text{Area}}$$

However, in this case, we are given the expression $9q^4r^6s^6$, which represents the area of the square piece of land. To find the length of one side, we need to take the square root of the expression.

Q: How do I take the square root of an expression with variables?

A: To take the square root of an expression with variables, we need to take the square root of each variable and then multiply the results. For example, if we have the expression $q^4$, we can take the square root of each variable as follows:

$$\sqrt{q^4} = q^2$$

Q: What is the difference between the square root and the absolute value?

A: The square root and the absolute value are two different mathematical operations.

• The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4, because 4 multiplied by 4 equals 16.
• The absolute value of a number is its distance from zero on the number line, without considering direction. For example, the absolute value of -3 is 3, because it is 3 units away from zero.

In the context of this problem, we need to take the square root of each variable and then multiply the results. However, we also need to consider the absolute value of each variable, because the length of a side cannot be negative.

Q: How do I know which option is correct?

A: To determine which option is correct, we need to compare our answer with the other options. In this case, we compared our answer with options A and B, and found that our answer is different from both options.

Q: What are some real-world applications of this concept?

A: This concept has many real-world applications, such as:

• Real estate: When buying or selling a piece of land, it's essential to know the length of one side of the property.
• Architecture: When designing a building, architects need to consider the length of one side of the property to ensure that the building fits within the available space.
• Engineering: Engineers need to consider the length of one side of a piece of land when designing infrastructure projects, such as roads or bridges.

Q: Can you provide more examples of how to calculate the length of one side of a square piece of land?

A: Yes, here are a few more examples:

• If the area of a square piece of land is $16x^4y^6$, what is the length of one side?
  • Answer: $4x^2y^3$
• If the area of a square piece of land is $25z^8w^4$, what is the length of one side?
  • Answer: $5z^4w^2$

Q: Can you provide a summary of the key points?

A: Yes, here is a summary of the key points:

• The formula for finding the length of one side of a square piece of land is $\text{Length} = \sqrt{\text{Area}}$.
• To take the square root of an expression with variables, we need to take the square root of each variable and then multiply the results.
• We need to consider the absolute value of each variable, because the length of a side cannot be negative.
• This concept has many real-world applications, such as real estate, architecture, and engineering.

References

• [1] Algebraic expressions and equations
• [2] Square roots and absolute values
• [3] Calculating the length of one side of a square piece of land

Related Articles

• [Calculating the Area of a Square Piece of Land](link to article)
• [Understanding Algebraic Expressions and Equations](link to article)
• [Square Roots and Absolute Values: A Comprehensive Guide](link to article)