which inequalities are true? select the four correct answers. $0

Question

which inequalities are true? select the four correct answers. $0 < \sqrt{8}$ $\sqrt{8} < 3$ $\sqrt{8} > \sqrt{7}$ $\sqrt{8} < 2$ $\sqrt{8} > 8$ $1 < \sqrt{8}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Square Root Estimation", "Radical Inequalities" ], "new_concepts": [], "current_concepts": [ "Square Root Estimation", "Radical Inequalities" ] } ## Estimate the value of the square root of 8 $$ \begin{aligned} &4 < 8 < 9 \ &\sqrt{4} < \sqrt{8} < \sqrt{9} \ &2 < \sqrt{8} < 3 \ &\sqrt{8} \approx 2.83 \end{aligned} $$ ## Evaluate each inequality statement $$ \begin{aligned} &0 < \sqrt{8} \implies 0 < 2.83 \quad (\text{True}) \ &\sqrt{8} < 3 \implies 2.83 < 3 \quad (\text{True}) \ &\sqrt{8} > \sqrt{7} \implies 8 > 7 \quad (\text{True}) \ &\sqrt{8} < 2 \implies 2.83 < 2 \quad (\text{False}) \ &\sqrt{8} > 8 \implies 2.83 > 8 \quad (\text{False}) \ &1 < \sqrt{8} \implies 1 < 2.83 \quad (\text{True}) \end{aligned} $$ ## Identify the four true inequalities $$ \text{True statements: } 0 < \sqrt{8},\ \sqrt{8} < 3,\ \sqrt{8} > \sqrt{7},\ 1 < \sqrt{8} $$

$0 < \sqrt{8}$

$\sqrt{8} < 3$

$\sqrt{8} > \sqrt{7}$

$\sqrt{8} < 2$

$\sqrt{8} > 8$

$1 < \sqrt{8}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Radical Inequalities" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Estimate the value of the square root of 8

Evaluate each inequality statement

Identify the four true inequalities

Answer: