which two numbers does $\sqrt{52}$ lie between on a number line?

7.0 and 7.1
7.1 and 7.2
7.2 and 7.3
7.3 and 7.4

Question

which two numbers does $\sqrt{52}$ lie between on a number line?

7.0 and 7.1
7.1 and 7.2
7.2 and 7.3
7.3 and 7.4

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Square Root Estimation" ], "current_concepts": [ "Square Root Estimation", "Number Line Representation" ] } ## Square the boundary values $$ \begin{aligned} 7.0^2 &= 49.00 \ 7.1^2 &= 50.41 \ 7.2^2 &= 51.84 \ 7.3^2 &= 53.29 \ 7.4^2 &= 54.76 \end{aligned} $$ ## Compare the squares to the target value $$ 51.84 < 52 < 53.29 $$ ## Take the square root of the inequality $$ \sqrt{51.84} < \sqrt{52} < \sqrt{53.29} \implies 7.2 < \sqrt{52} < 7.3 $$

7.0 and 7.1

7.1 and 7.2

7.2 and 7.3

7.3 and 7.4

{ "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 squares to the target value

Take the square root of the inequality

Answer: