Chapter 10 - Radical Expressions and Equations - 10-1 The Pythagorean Theorem - Practice and Problem-Solving Exercises - Page 617: 32

Not a Pythagorean Triple.

The Pythagorean Theorem states that for a right triangle, $a^{2} +b^{2} = c^{2}$. In order to figure out if these sides can be a Pythagorean Triple, we plug them into the Pythagorean Theorem: $40^{2} + 41^{2} = 58^{2} \\\\ 3821=3364$ This is not true, so it is not a Pythagorean Triple.