The Area Of A Square Piece Of Land In Square Units Can Be Represented By The Expression 9 Q 4 R 8 S 6 9q^4r^8s^6 9 Q 4 R 8 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.

Introduction

When it comes to calculating the area of a square piece of land, we often encounter expressions that involve variables and exponents. In this article, we will explore how to find the length of one side of a square piece of land given the expression $9q^4r^8s^6$.

Understanding the Expression

The given expression $9q^4r^8s^6$ represents the area of a square piece of land in square units. To find the length of one side, we need to understand the relationship between the area and the side length of a square.

The Formula for the Area of a Square

The formula for the area of a square is given by:

$$A = s^2$$

where $A$ is the area and $s$ is the length of one side.

Finding the Length of One Side

To find the length of one side, we need to take the square root of the area. In this case, we have:

$$A = 9q^4r^8s^6$$

Taking the square root of both sides, we get:

$$s = \sqrt{9q^4r^8s^6}$$

Simplifying the Expression

To simplify the expression, we can rewrite the square root as:

$$s = \sqrt{9} \cdot \sqrt{q^4} \cdot \sqrt{r^8} \cdot \sqrt{s^6}$$

Using the property of square roots, we can rewrite the expression as:

$$s = 3q^2r^4s^3$$

Removing the Absolute Value

Since the length of one side cannot be negative, we can remove the absolute value by taking the positive square root:

$$s = 3q^2r^4s^3$$

Comparing with the Options

Now, let's compare our result with the options:

A. $3q^2r^6|s^3|$ units B. $3q^2r^4|s^3|$ units C. $3q^2r^4s^3$ units

Our result matches option C.

Conclusion

In conclusion, the length of one side of the square piece of land is given by $3q^2r^4s^3$ units.

Final Answer

The final answer is $3q^2r^4s^3$ units.

Discussion

This problem requires a good understanding of the relationship between the area and the side length of a square. It also requires the ability to simplify expressions and remove absolute values.

Related Topics

• Area of a square
• Square root
• Simplifying expressions
• Removing absolute values

Practice Problems

1. Find the length of one side of a square piece of land with an area of $16x^4y^6$.
2. Find the length of one side of a square piece of land with an area of $25z^8w^4$.

Solutions

1. $4x^2y^3$
2. $5z^4w^2$

References

• [1] "Area of a Square" by Math Open Reference
• [2] "Square Root" by Khan Academy

Introduction

In our previous article, we explored how to find the length of one side of a square piece of land given the expression $9q^4r^8s^6$. In this article, we will answer some frequently asked questions related to the area of a square piece of land.

Q&A

Q: What is the formula for the area of a square?

A: The formula for the area of a square is given by:

$$A = s^2$$

where $A$ is the area and $s$ is the length of one side.

Q: How do I find the length of one side of a square piece of land?

A: To find the length of one side, you need to take the square root of the area. In this case, we have:

$$A = 9q^4r^8s^6$$

Taking the square root of both sides, we get:

$$s = \sqrt{9q^4r^8s^6}$$

Q: Can I remove the absolute value when finding the length of one side?

A: Yes, since the length of one side cannot be negative, we can remove the absolute value by taking the positive square root.

Q: What if the area is given in terms of multiple variables?

A: In that case, you need to simplify the expression and remove any absolute values before finding the length of one side.

Q: Can I use this method to find the length of one side of a rectangle?

A: No, this method is only applicable to squares. To find the length of one side of a rectangle, you need to use a different formula.

Q: What if the area is given in terms of a negative number?

A: In that case, you need to take the absolute value of the area before finding the length of one side.

Q: Can I use this method to find the area of a square given the length of one side?

A: No, this method is only applicable to finding the length of one side given the area. To find the area of a square given the length of one side, you need to use the formula:

$$A = s^2$$

Q: What if I have a square piece of land with an area of $16x^4y^6$?

A: To find the length of one side, you need to take the square root of the area:

$$s = \sqrt{16x^4y^6}$$

Simplifying the expression, you get:

$$s = 4x^2y^3$$

Q: What if I have a square piece of land with an area of $25z^8w^4$?

A: To find the length of one side, you need to take the square root of the area:

$$s = \sqrt{25z^8w^4}$$

Simplifying the expression, you get:

$$s = 5z^4w^2$$

Conclusion

In conclusion, finding the length of one side of a square piece of land requires a good understanding of the relationship between the area and the side length of a square. It also requires the ability to simplify expressions and remove absolute values.

Final Answer

The final answer is that the length of one side of a square piece of land can be found by taking the square root of the area and removing any absolute values.

Discussion

This article provides a comprehensive guide to finding the length of one side of a square piece of land. It also answers some frequently asked questions related to the area of a square piece of land.

Related Topics

• Area of a square
• Square root
• Simplifying expressions
• Removing absolute values

Practice Problems

1. Find the length of one side of a square piece of land with an area of $36x^6y^8$.
2. Find the length of one side of a square piece of land with an area of $49z^4w^6$.

Solutions

1. $6x^3y^4$
2. $7z^2w^3$

References

• [1] "Area of a Square" by Math Open Reference
• [2] "Square Root" by Khan Academy