Question
Is (5, 7, V74) a Pythagorean triple? Enter 1 for yes or 2 for no. (1-point)
Answers
GPT-4o mini
To determine if the triplet (5, 7, V74) forms a Pythagorean triple, we use the Pythagorean theorem: \( a^2 + b^2 = c^2 \), where \( c \) is the largest number.
In this case, we identify:
- \( a = 5 \)
- \( b = 7 \)
- \( c = \sqrt{74} \)
Now we check if \( 5^2 + 7^2 = (\sqrt{74})^2 \):
1. Calculate \( 5^2 \):
\[
5^2 = 25
\]
2. Calculate \( 7^2 \):
\[
7^2 = 49
\]
3. Add \( 5^2 \) and \( 7^2 \):
\[
25 + 49 = 74
\]
4. Calculate \( (\sqrt{74})^2 \):
\[
(\sqrt{74})^2 = 74
\]
Since \( 25 + 49 = 74 \), it follows that \( 5^2 + 7^2 = (\sqrt{74})^2 \).
Therefore, (5, 7, V74) is a Pythagorean triple.
The answer is **1** (for yes).
In this case, we identify:
- \( a = 5 \)
- \( b = 7 \)
- \( c = \sqrt{74} \)
Now we check if \( 5^2 + 7^2 = (\sqrt{74})^2 \):
1. Calculate \( 5^2 \):
\[
5^2 = 25
\]
2. Calculate \( 7^2 \):
\[
7^2 = 49
\]
3. Add \( 5^2 \) and \( 7^2 \):
\[
25 + 49 = 74
\]
4. Calculate \( (\sqrt{74})^2 \):
\[
(\sqrt{74})^2 = 74
\]
Since \( 25 + 49 = 74 \), it follows that \( 5^2 + 7^2 = (\sqrt{74})^2 \).
Therefore, (5, 7, V74) is a Pythagorean triple.
The answer is **1** (for yes).