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", "Number Line Representation" ] } ## Square the boundary values $$ \begin{aligned} 11.3^2 &= 127.69 \ 11.4^2 &= 129.96 \end{aligned} $$ ## Compare the squared values with 128 $$ 127.69 < 128 < 129.96 $$ ## Take the square root of each term $$ 11.3 < \sqrt{128} < 11.4 $$

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:

Square the boundary values

Compare the squared values with 128

Take the square root of each term

Answer: