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

* 0.2
* 0.4
* 1.5
* 1.7

Question

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", "Number Line Representation" ], "new_concepts": [], "current_concepts": [ "Square Root Estimation", "Number Line Representation" ] } ## Estimate the values of the square roots $$ \begin{aligned} &3.4^2 = 11.56,\quad 3.5^2 = 12.25 \implies \sqrt{12} \approx 3.5\ &3.8^2 = 14.44,\quad 3.9^2 = 15.21 \implies \sqrt{15} \approx 3.9 \end{aligned} $$ ## Calculate the difference $$ 3.9 - 3.5 = 0.4 $$ ## Verify with the number line representation $$ \begin{aligned} &\text{Interval between } 3 \text{ and } 4 \text{ is divided into } 10 \text{ equal parts (tenths).}\ &\sqrt{12} \text{ is plotted at } 3.5.\ &\sqrt{15} \text{ is plotted at } 3.9.\ &\text{Distance} = 3.9 - 3.5 = 0.4 \end{aligned} $$

0.2

0.4

1.5

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 values of the square roots

Calculate the difference

Verify with the number line representation

Answer: