Question

Is (5,7,74−−√)  a Pythagorean triple? Enter 1 for yes or 2 for no.

Answer 1

To determine if \((5, 7, \sqrt{74})\) is a Pythagorean triple, we need to check if the relationship \(a^2 + b^2 = c^2\) holds, where \(a\) and \(b\) are the two smaller numbers and \(c\) is the largest number.

Here, we have:
- \(a = 5\)
- \(b = 7\)
- \(c = \sqrt{74}\)

Now we calculate \(a^2 + b^2\) and \(c^2\):

1. Calculate \(a^2\) and \(b^2\):
\[
a^2 = 5^2 = 25
\]
\[
b^2 = 7^2 = 49
\]

2. Now add these two values:
\[
a^2 + b^2 = 25 + 49 = 74
\]

3. Calculate \(c^2\):
\[
c^2 = (\sqrt{74})^2 = 74
\]

Since \(a^2 + b^2 = 74\) and \(c^2 = 74\), we find that:
\[
a^2 + b^2 = c^2
\]

This confirms that \((5, 7, \sqrt{74})\) is indeed a Pythagorean triple.

Therefore, the answer is **1** (for yes).