`(3,4,5),\ (5, 12 , 13),\ (8, 15 ,\ 17)` etc. are Pythagorean triplets, because `3^2+4^2=25=5^2` `5^2+12^2=169=13^2` `8^2+15^2=289=17^2`

Explanation

To show that the sets of numbers (3, 4, 5), (5, 12, 13), and (8, 15, 17) are Pythagorean triplets, we need to verify the Pythagorean theorem, which states that for a triplet (a, b, c), if \( a^2 + b^2 = c^2 \), then (a, b, c) is a Pythagorean triplet.

### Step-by-Step Solution:

1. **Check the first triplet (3, 4, 5)**:
- Calculate \( 3^2 \):
\[
3^2 = 9
...