which two numbers does $\sqrt{128}$ lie between on a number line?

11.0 and 11.1
11.2 and 11.3
11.3 and 11.4
11.4 and 11.5

Question

which two numbers does $\sqrt{128}$ lie between on a number line?

11.0 and 11.1
11.2 and 11.3
11.3 and 11.4
11.4 and 11.5

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" ], "new_concepts": [], "current_concepts": [ "Square Root Estimation", "Perfect Squares" ] } ## Identify bounding perfect squares $$ \begin{aligned} 11^2 &= 121 \ 12^2 &= 144 \ 121 &< 128 < 144 \ 11 &< \sqrt{128} < 12 \end{aligned} $$ ## Evaluate squares of decimal options $$ \begin{aligned} 11.3^2 &= 127.69 \ 11.4^2 &= 129.96 \end{aligned} $$ ## Compare values to locate interval $$ \begin{aligned} 127.69 &< 128 < 129.96 \ 11.3 &< \sqrt{128} < 11.4 \end{aligned} $$

11.0 and 11.1

11.2 and 11.3

11.3 and 11.4

11.4 and 11.5

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

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QUESTION IMAGE

Question

Explanation:

Identify bounding perfect squares

Evaluate squares of decimal options

Compare values to locate interval

Answer: