Question

Name all sets of numbers each of the following real numbers belongs to (natural, whole, integer, rational, and/or irrational). Briefly explain how we know the number belongs to each identified set.
a) -√81
b)√19
c)0.020202…

Answer 1

Explicație pas cu pas:

a)

$- \sqrt{81} = - \sqrt{ {9}^{2} } = - 9$

$- \sqrt{81} \in \mathbb{Z} \\ - \sqrt{81} \in \mathbb{Q} \\ - \sqrt{81} \in \mathbb{R}$

b)

$\mathbb{I} = \mathbb{R{/}Q}$

$\sqrt{19} \in \mathbb{I} \ \\ \sqrt{19} \in \mathbb{R}$

c)

$0.020202... = 0.(02) = \dfrac{2}{99}$

$0.020202... \in \mathbb{Q} \\ 0.020202... \in \mathbb{R}$