Which graphThe Pythagorean theorem states that the sum of the squares of the legs of a right triangle is equal to the square of
the hypotenuse by the formula a2 + b2 = c2. If a is a rational number and b is a rational number, why could c be an irrational number? represents the solution set of the compound inequality mc011-1.jpg?
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