Question

Vocabulary Terms - Define/Illustrate
Interpreting Irrational answers for side lengths of squares and cubes.
Interpreting Irrational answers for time and money
If you apply a formula and your answer is $√65 . How much money is that?

Xander plans to raise hogs. He builds a pig pen 23’ x 32’ and knows that each pig requires about 6 ft.^2 space. How many pigs can he fit in the pen?

Answer 1

### Vocabulary Terms - Definitions and Illustrations

**Interpreting Irrational Answers for Side Lengths of Squares and Cubes:**
- **Definition**: When you calculate the side length of a square or the edge length of a cube and obtain an irrational number (a number that cannot be expressed as a simple fraction, e.g., \( \sqrt{2}, \pi, e \)), you need to interpret this result in the context of geometry.
- **Illustration**: For instance, if you find the side length of a square that has an area of 2, you'd use the formula:
\[
\text{Area} = \text{side}^2 \implies \text{side} = \sqrt{2}
\]
The approximate value of \( \sqrt{2} \) is about 1.414. In practice, you would approximate this to a decimal value when measuring, indicating that the side is about 1.414 units long, which is meaningful for physical dimensions.

**Interpreting Irrational Answers for Time and Money:**
- **Definition**: Similar to the geometric case, if time or money is expressed as an irrational number, you typically want to round it to the nearest cent or second for practical use.
- **Illustration**: If a calculation yields \( \sqrt{65} \) hours, you would first calculate its approximate value:
\[
\sqrt{65} \approx 8.06
\]
Thus, you could interpret this result as approximately 8 hours and 4 minutes.

### Applying the Formula for Money
If you apply a formula and your answer is \( \sqrt{65} \), then to interpret how much money that is:
1. Calculate the approximate value:
\[
\sqrt{65} \approx 8.062
\]
2. You can interpret this as approximately $8.06 when rounded to the nearest cent.

### Problem: Xander’s Pig Pen
Xander plans to build a pig pen that is 23 feet by 32 feet. To determine how many pigs can fit within this space, follow these steps:

1. **Calculate the Area of the Pig Pen**:
\[
\text{Area} = \text{Length} \times \text{Width} = 23\, \text{ft} \times 32\, \text{ft} = 736\, \text{ft}^2
\]

2. **Determine the Space Required per Pig**:
Each pig requires 6 ft² of space.

3. **Calculate the Number of Pigs that Fit in the Pen**:
\[
\text{Number of Pigs} = \frac{\text{Total Area of Pen}}{\text{Area Required per Pig}} = \frac{736\, \text{ft}^2}{6\, \text{ft}^2} \approx 122.67
\]

Since you cannot have a fraction of a pig, Xander can fit a maximum of **122 pigs** in the pen while ensuring each pig has the required space.