Question

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

Answer 1

To determine if (5, 7, √74) is a Pythagorean triple, we check if the square of the largest number (√74) equals the sum of the squares of the other two numbers (5 and 7):

1. Calculate \(5^2 + 7^2\):
\[
5^2 = 25
\]
\[
7^2 = 49
\]
\[
5^2 + 7^2 = 25 + 49 = 74
\]

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

Now we compare the two results:
\[
5^2 + 7^2 = 74 \quad \text{and} \quad (\sqrt{74})^2 = 74
\]

Since both are equal, (5, 7, √74) satisfies the condition of a Pythagorean triple.

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