Question

Select all the statements that are true.
π
is irrational because π
is a repeating decimal.
7–√
is irrational because 7 is not a perfect square.
7.1234… is irrational because it is a nonterminating, nonrepeating decimal.
7–√
is rational because 7 is not a perfect square.
π
is irrational because π
is not a repeating decimal.

Answer 1

True statements: 2, 3, and 5.

- (2) √7 is irrational because 7 is not a perfect square. True: if n is an integer that is not a perfect square, √n is irrational.
- (3) 7.1234… is irrational because it is a nonterminating, nonrepeating decimal. True: any nonterminating, nonrepeating decimal represents an irrational number.
- (5) π is irrational because π is not a repeating decimal. True: a decimal that does not terminate or repeat cannot be rational, so a nonrepeating decimal expansion (as π has) implies irrationality.

False statements:
- (1) is false: a repeating decimal is rational, not a reason for irrationality.
- (4) is false: √7 is not rational (so the conclusion is wrong).