which inequalities are true? select the four correct answers.

$\sqrt{5}

Question

which inequalities are true? select the four correct answers.

$\sqrt{5} < 2.3 <
\sqrt{6}$

$\sqrt{5} < 2.4 < \sqrt{6}$

$\sqrt{4} < \sqrt{5} < \sqrt{5.5}$

$\sqrt{8} < 3 < \sqrt{9}$

$\sqrt{8} < 2.9 < \sqrt{9}$

$\sqrt{4} < 4.5 < \sqrt{5}$

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" ] } ## Square all terms in each inequality $$ \begin{aligned} &\text{Option 1: } \sqrt{5} < 2.3 < \sqrt{6} \implies 5 < 2.3^2 < 6 \implies 5 < 5.29 < 6 \quad (\text{True}) \ &\text{Option 2: } \sqrt{5} < 2.4 < \sqrt{6} \implies 5 < 2.4^2 < 6 \implies 5 < 5.76 < 6 \quad (\text{True}) \ &\text{Option 3: } \sqrt{4} < \sqrt{5} < \sqrt{5.5} \implies 4 < 5 < 5.5 \quad (\text{True}) \ &\text{Option 4: } \sqrt{8} < 3 < \sqrt{9} \implies 8 < 3^2 < 9 \implies 8 < 9 < 9 \quad (\text{False}) \ &\text{Option 5: } \sqrt{8} < 2.9 < \sqrt{9} \implies 8 < 2.9^2 < 9 \implies 8 < 8.41 < 9 \quad (\text{True}) \ &\text{Option 6: } \sqrt{4} < 4.5 < \sqrt{5} \implies 4 < 4.5^2 < 5 \implies 4 < 20.25 < 5 \quad (\text{False}) \end{aligned} $$

(A) $\sqrt{5} < 2.3 < \sqrt{6}$

(B) $\sqrt{5} < 2.4 < \sqrt{6}$

(C) $\sqrt{4} < \sqrt{5} < \sqrt{5.5}$

(D) $\sqrt{8} < 3 < \sqrt{9}$

(E) $\sqrt{8} < 2.9 < \sqrt{9}$

(F) $\sqrt{4} < 4.5 < \sqrt{5}$

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

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QUESTION IMAGE

Question

Explanation:

Square all terms in each inequality

Answer: