Questions: Tell whether each number is an element of N (a natural number), Z (an integer), Q (a rational number), Q' (an irrational number), or R (a real number). Since these sets are not all disjoint, you may need to list more than one set for each answer. (Select all that apply.) (a) 15 (b) 5.58 Q Q' R (c) 1.5656565656... N Z Q Q' R (d) sqrt(8) N Q Q' R (e) (f) 0.00(42) Z Q Q' R (g) sqrt(36) Z Q Q' R (h) sqrt(1,000) N Z Q Q' R (i) 1/2 N Z Q Q' R

Transcript text: Tell whether each number is an element of $\mathbb{N}$ (a natural number), $\mathbb{Z}$ (an integer), $\mathbb{Q}$ (a rational number), $\mathbb{Q}^{\prime}$ (an irrational number), or $\mathbb{R}$ (a real number). Since these sets are not all disjoint, you may need to list more than one set for each answer. (Select all that apply.) (a) 15 (b) 5.58 $\mathbb{Q}$ $\mathbb{Q}^{\prime}$ $\mathbb{R}$ (c) $1.5656565656 \ldots$ $\mathbb{N}$ $\mathbb{Z}$ $\mathbb{Q}$ $\mathbb{Q}^{\prime}$ $\mathbb{R}$ (d) $\sqrt{8}$ $\mathbb{N}$ $\mathbb{Q}$ $\mathbb{Q}^{\prime}$ $\mathbb{R}$ (e) (f) \[ 0.00 \overline{42} \] $\mathbb{Z}$ $\mathbb{Q}$ $\mathbb{Q}^{\prime}$ $\mathbb{R}$ (g) $\sqrt{36}$ $\mathbb{Z}$ $\mathbb{Q}$ $\mathbb{Q}^{\prime}$ $\mathbb{R}$ (h) $\sqrt{1,000}$ $\mathbb{N}$ $\mathbb{Z}$ $\mathbb{Q}$ $\mathbb{Q}^{\prime}$ $\mathbb{R}$ (i) $\frac{1}{2}$ $\mathbb{N}$ $\mathbb{Z}$ $\mathbb{Q}$ $\mathbb{Q}^{\prime}$ $\mathbb{R}$