Question
4 of 4
Scroll Up
Brittany is making a square garden. She wants to be sure that each side of the garden measures as a rational number. Which of the following values could be the area of Brittany's garden, in inches?
53
64
79
97
Scroll Up
Brittany is making a square garden. She wants to be sure that each side of the garden measures as a rational number. Which of the following values could be the area of Brittany's garden, in inches?
53
64
79
97
Answers
GPT-4o mini
To determine which values could be the area of Brittany's square garden where each side measures a rational number, we need to consider that the area \( A \) of a square with side length \( s \) is given by the formula:
\[ A = s^2 \]
For \( s \) to be a rational number, \( A \) must be a perfect square, meaning that the area must be expressible as the square of a rational number.
Now we check the provided options to see which ones are perfect squares:
1. **53**:
- The square root of 53 is approximately 7.28, which is not an integer. Hence, it is not a perfect square.
2. **64**:
- The square root of 64 is 8, which is an integer. Therefore, 64 is a perfect square.
3. **79**:
- The square root of 79 is approximately 8.83, which is not an integer. Hence, it is not a perfect square.
4. **97**:
- The square root of 97 is approximately 9.85, which is not an integer. Hence, it is not a perfect square.
Out of the options given, the only value that could be the area of Brittany's garden, where each side measures a rational number, is:
**64**
\[ A = s^2 \]
For \( s \) to be a rational number, \( A \) must be a perfect square, meaning that the area must be expressible as the square of a rational number.
Now we check the provided options to see which ones are perfect squares:
1. **53**:
- The square root of 53 is approximately 7.28, which is not an integer. Hence, it is not a perfect square.
2. **64**:
- The square root of 64 is 8, which is an integer. Therefore, 64 is a perfect square.
3. **79**:
- The square root of 79 is approximately 8.83, which is not an integer. Hence, it is not a perfect square.
4. **97**:
- The square root of 97 is approximately 9.85, which is not an integer. Hence, it is not a perfect square.
Out of the options given, the only value that could be the area of Brittany's garden, where each side measures a rational number, is:
**64**