the values $\sqrt{12}$ and $\sqrt{15}$ are plotted on the number line.

what is the approximate difference in tenths between $\sqrt{12}$ and $\sqrt{15}$?

0.2
0.4
1.5
1.7

Question

the values $\sqrt{12}$ and $\sqrt{15}$ are plotted on the number line.

what is the approximate difference in tenths between $\sqrt{12}$ and $\sqrt{15}$?

0.2
0.4
1.5
1.7

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" ] } ## Estimate the square roots to the nearest tenth $$ \begin{aligned} &3.4^2 = 11.56,\quad 3.5^2 = 12.25 \implies \sqrt{12} \approx 3.5 \ &3.8^2 = 14.44,\quad 3.9^2 = 15.21 \implies \sqrt{15} \approx 3.9 \end{aligned} $$ ## Calculate the difference $$ \sqrt{15} - \sqrt{12} \approx 3.9 - 3.5 = 0.4 $$ ## Match with the given options $$ \text{The calculated difference of } 0.4 \text{ matches option 2.} $$

(A) 0.2

(B) 0.4

(C) 1.5

(D) 1.7

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

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QUESTION IMAGE

Question

Explanation:

Estimate the square roots to the nearest tenth

Calculate the difference

Match with the given options

Answer: