pairs

irrational numbers $\longrightarrow$
rational numbers $\longrightarrow$
real numbers $\longrightarrow$
integers $\longrightarrow$

tiles
$\{-227, 4, 19, 28\}$
$\{\sqrt{36}, \frac{1}{6}, 0.245, -15\}$
$\{\pi, \frac{\sqrt{3}}{2}, 6.283185..., -\sqrt{6}\}$
$\{-\frac{3}{25}, \frac{2\pi}{3}, \sqrt{16}, \frac{2}{\sqrt{5}}\}$

Question

pairs

irrational numbers $\longrightarrow$
rational numbers $\longrightarrow$
real numbers $\longrightarrow$
integers $\longrightarrow$

tiles
$\{-227, 4, 19, 28\}$
$\{\sqrt{36}, \frac{1}{6}, 0.245, -15\}$
$\{\pi, \frac{\sqrt{3}}{2}, 6.283185..., -\sqrt{6}\}$
$\{-\frac{3}{25}, \frac{2\pi}{3}, \sqrt{16}, \frac{2}{\sqrt{5}}\}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Number Classification", "Real Number Subsets" ], "new_concepts": [], "current_concepts": [ "Number Classification", "Real Number Subsets" ] } ## Classify each set of numbers $$ \begin{aligned} &S_1 = \{-227, 4, 19, 28\} \subset \mathbb{Z} \quad \text{(Integers)} \ &S_2 = \{\sqrt{36}, \frac{1}{6}, 0.245, -15\} = \{6, \frac{1}{6}, 0.245, -15\} \subset \mathbb{Q} \quad \text{(Rational numbers)} \ &S_3 = \{\pi, \frac{\sqrt{3}}{2}, 6.283185\dots, -\sqrt{6}\} \subset \mathbb{R} \setminus \mathbb{Q} \quad \text{(Irrational numbers)} \ &S_4 = \{-\frac{3}{25}, \frac{2\pi}{7}, \sqrt{16}, \frac{2}{\sqrt{5}}\} = \{-\frac{3}{25}, \frac{2\pi}{7}, 4, \frac{2}{\sqrt{5}}\} \subset \mathbb{R} \quad \text{(Real numbers)} \end{aligned} $$ ## Match categories to tiles $$ \begin{aligned} &\text{irrational numbers} \longrightarrow \{\pi, \frac{\sqrt{3}}{2}, 6.283185\dots, -\sqrt{6}\} \ &\text{rational numbers} \longrightarrow \{\sqrt{36}, \frac{1}{6}, 0.245, -15\} \ &\text{real numbers} \longrightarrow \{-\frac{3}{25}, \frac{2\pi}{7}, \sqrt{16}, \frac{2}{\sqrt{5}}\} \ &\text{Integers} \longrightarrow \{-227, 4, 19, 28\} \end{aligned} $$ * **irrational numbers** $\longrightarrow$ $\{\pi, \frac{\sqrt{3}}{2}, 6.283185\dots, -\sqrt{6}\}$ * **rational numbers** $\longrightarrow$ $\{\sqrt{36}, \frac{1}{6}, 0.245, -15\}$ * **real numbers** $\longrightarrow$ $\{-\frac{3}{25}, \frac{2\pi}{7}, \sqrt{16}, \frac{2}{\sqrt{5}}\}$ * **Integers** $\longrightarrow$ $\{-227, 4, 19, 28\}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Number Classification" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Classify each set of numbers

Match categories to tiles

Answer: