which statements are true? select the five correct answers. $\sqrt{1.8} 1$ $\sqrt{1.8}

Question

which statements are true? select the five correct answers.

\$\sqrt{1.8} < 1.8\$

\$\sqrt{1.8} > 1\$

\$\sqrt{1.8} < \sqrt{1.9}\$

\$1.3 < \sqrt{1.8} < 1.4\$

\$\sqrt{1.9} + \sqrt{1.8} > 2\$

\$\sqrt{1.9} - \sqrt{1.8} > 0.1\$

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", "Properties of Radicals" ] } ## Evaluate the first four statements $$ \begin{aligned} &\text{Statement 1: } \sqrt{1.8} < 1.8 \implies 1.8 < 1.8^2 = 3.24 \quad (\text{True}) \ &\text{Statement 2: } \sqrt{1.8} > 1 \implies 1.8 > 1^2 = 1 \quad (\text{True}) \ &\text{Statement 3: } \sqrt{1.8} < \sqrt{1.9} \implies 1.8 < 1.9 \quad (\text{True}) \ &\text{Statement 4: } 1.3 < \sqrt{1.8} < 1.4 \implies 1.3^2 = 1.69 < 1.8 < 1.4^2 = 1.96 \quad (\text{True}) \end{aligned} $$ ## Evaluate the last two statements $$ \begin{aligned} &\text{Statement 5: } \sqrt{1.9} + \sqrt{1.8} > 2 \implies \text{Since } \sqrt{1.9} > 1.3 \text{ and } \sqrt{1.8} > 1.3, \text{ their sum is } > 2.6 > 2 \quad (\text{True}) \ &\text{Statement 6: } \sqrt{1.9} - \sqrt{1.8} > 0.1 \implies \sqrt{1.9} - \sqrt{1.8} = \frac{0.1}{\sqrt{1.9} + \sqrt{1.8}} < \frac{0.1}{2.6} < 0.1 \quad (\text{False}) \end{aligned} $$

(A) $\sqrt{1.8} < 1.8$

(B) $\sqrt{1.8} > 1$

(C) $\sqrt{1.8} < \sqrt{1.9}$

(D) $1.3 < \sqrt{1.8} < 1.4$

(E) $\sqrt{1.9} + \sqrt{1.8} > 2$

(F) $\sqrt{1.9} - \sqrt{1.8} > 0.1$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Square Root Estimation" ] }

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Question

Explanation:

Evaluate the first four statements

Evaluate the last two statements

Answer: