Question
Is (5, 7, sqrt 74) a Pythagorean triple?
Answers
GPT-4o mini
To determine if the triplet \((5, 7, \sqrt{74})\) is a Pythagorean triple, we need to check if the square of the longest side equals the sum of the squares of the other two sides.
Here, the longest side is \(\sqrt{74}\). We will compare:
\[
a^2 + b^2 = c^2
\]
where \(a = 5\), \(b = 7\), and \(c = \sqrt{74}\).
First, we calculate \(a^2 + b^2\):
\[
5^2 + 7^2 = 25 + 49 = 74
\]
Next, we calculate \(c^2\):
\[
(\sqrt{74})^2 = 74
\]
Now we check if \(a^2 + b^2 = c^2\):
\[
74 = 74
\]
Since both sides are equal, we conclude that \((5, 7, \sqrt{74})\) is indeed a Pythagorean triple.
Here, the longest side is \(\sqrt{74}\). We will compare:
\[
a^2 + b^2 = c^2
\]
where \(a = 5\), \(b = 7\), and \(c = \sqrt{74}\).
First, we calculate \(a^2 + b^2\):
\[
5^2 + 7^2 = 25 + 49 = 74
\]
Next, we calculate \(c^2\):
\[
(\sqrt{74})^2 = 74
\]
Now we check if \(a^2 + b^2 = c^2\):
\[
74 = 74
\]
Since both sides are equal, we conclude that \((5, 7, \sqrt{74})\) is indeed a Pythagorean triple.