Question

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?

Answer 1

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