Because even though 'a' and 'b' are rational, and their squares are
also rational, that doesn't guarantee that the sum of their squares
has a rational square root.
Examples:
1 and 2
Sum of squares = 5
√5 is irrational
2 and 3
Sum of squares = 13
√13 is irrational
4 and 5
Sum of squares is 41
√41 is irrational
'c' is rational only when 'a', 'b', and 'c' form a . . . . . wait for it . . . . .
a 'Pythagorean triple'.
Examples:
3 and 4
Sum of squares is 25
√25 = 5 is rational yay
5 and 12
Sum of squares is 169
√169 = 13 is rational yay
