Question

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

Answer 1

To determine if the tuple (5, 7, √74) is a Pythagorean triple, we need to check if the sum of the squares of the two smaller numbers equals the square of the largest number.

First, identify the sides:
- a = 5
- b = 7
- c = √74 (assuming it's the hypotenuse)

Now, we check if \( a^2 + b^2 = c^2 \):

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

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

Now, compare the two results:
- \( a^2 + b^2 = 74 \)
- \( c^2 = 74 \)

Since \( a^2 + b^2 = c^2 \) holds true, (5, 7, √74) is indeed a Pythagorean triple.

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