Let a be a rational number and b be an irrational number. which of the following are true statements.
The sum of a and b is never rational
The product of a and b is rational
b squared is sometimes rational
a squared is always rational
The correct statements are:
- The sum of a and b is never rational: This statement is true. The sum of a rational number and an irrational number is always irrational.
- The product of a and b is irrational: This statement is true. The product of any non-zero rational number and an irrational number is always irrational.
- b squared is sometimes rational: This statement is true. Depending on the value of b, its square could be rational or irrational. For example, if b = sqrt(2), then b^2 = 2, which is rational. But if b = sqrt(3), then b^2 = 3, which is also rational.
- a squared is always rational: This statement is true. The square of any rational number is always rational.