5.05: Properties of Rational and Irrational Numbers

What number can you multiply by π to get a rational number? Select each correct answer.

0 and 1/π

Which equations support the fact that rational numbers are closed under addition? Select each correct answer.

1/3+1/3= 2/3 And √9+√9=2√9

Select from the drop-down menus to correctly identify whether the given operation is closed or not closed with respect to each set of numbers. Positive integers are _____ under subtraction. Rational numbers are _______ under multiplication. Negative real numbers are ________ under division. Irrational numbers are _______ under addition.

1: Not Closed 2: Closed 3: Not Closed 4: Not Closed

Select from the drop-down menus to correctly complete the proof. To prove that √2⋅7 is ________ irrational, assume the product is rational and set it equal to ​ a/b ​, where b is not equal to 0. Isolating the radical gives ​ √2=a/7b ​ . The right side of the equation is ______. Because the left side of the equation ______

1: Rational 2: Irrational 3: Irrational

Which expressions simplify to an irrational answer? Select each correct answer.

√3 • √2 And √7 • √5