Question
Is (5,7,74−−√) a Pythagorean triple? Enter 1 for yes or 2 for no.(1 point)
Answers
GPT-4o mini
To determine if \((5, 7, \sqrt{74})\) is a Pythagorean triple, we check if the equation \(a^2 + b^2 = c^2\) holds, where \(c\) is the largest number.
Here, \(a = 5\), \(b = 7\), and \(c = \sqrt{74}\).
Now, we calculate the squares:
1. \(a^2 = 5^2 = 25\)
2. \(b^2 = 7^2 = 49\)
3. \(c^2 = (\sqrt{74})^2 = 74\)
Now, add \(a^2\) and \(b^2\):
\[
25 + 49 = 74
\]
Next, we see if this holds:
\[
a^2 + b^2 = c^2 \implies 25 + 49 = 74
\]
Since this is true, \((5, 7, \sqrt{74})\) is indeed a Pythagorean triple.
Therefore, the answer is **1** (for yes).
Here, \(a = 5\), \(b = 7\), and \(c = \sqrt{74}\).
Now, we calculate the squares:
1. \(a^2 = 5^2 = 25\)
2. \(b^2 = 7^2 = 49\)
3. \(c^2 = (\sqrt{74})^2 = 74\)
Now, add \(a^2\) and \(b^2\):
\[
25 + 49 = 74
\]
Next, we see if this holds:
\[
a^2 + b^2 = c^2 \implies 25 + 49 = 74
\]
Since this is true, \((5, 7, \sqrt{74})\) is indeed a Pythagorean triple.
Therefore, the answer is **1** (for yes).