Some right triangles have integer sides. The most common triples are (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25).
Any multiple of a triple is also a triple. Since (3, 4, 5) works, so does (6, 8, 10) and (9, 12, 15). Recognizing these patterns saves calculation time.
When a problem gives you sides 6 and 8, you know the hypotenuse is 10 without computing the square root.