Question

is 5, 7 √74 a pythagorean triple

Answer 1

To determine if \(5, 7, \sqrt{74}\) forms a Pythagorean triple, we need to check if the square of the largest number equals the sum of the squares of the other two numbers.

Here, \( \sqrt{74} \) is the largest number. We will check if:

\[
\sqrt{74}^2 = 5^2 + 7^2
\]

Calculating each side:

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

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

3. Sum the squares of \(5\) and \(7\):
\[
5^2 + 7^2 = 25 + 49 = 74
\]

Now, we compare both sides:

\[
\sqrt{74}^2 = 74
\]
\[
5^2 + 7^2 = 74
\]

Since both sides are equal, \(5, 7, \sqrt{74}\) does indeed form a Pythagorean triple.