the values $\sqrt{8}$ and $\sqrt{14}$ are plotted on the number line.

what is the approximate difference in tenths between the two values?

0.5
0.9
1.1
2.4

Question

the values $\sqrt{8}$ and $\sqrt{14}$ are plotted on the number line.

what is the approximate difference in tenths between the two values?

0.5
0.9
1.1
2.4

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 values of the square roots to the nearest tenth $$ \begin{aligned} &2.8^2 = 7.84,\quad 2.9^2 = 8.41 \implies \sqrt{8} \approx 2.8 \ &3.7^2 = 13.69,\quad 3.8^2 = 14.44 \implies \sqrt{14} \approx 3.7 \end{aligned} $$ ## Calculate the difference between the estimated values $$ \sqrt{14} - \sqrt{8} \approx 3.7 - 2.8 = 0.9 $$

0.5

0.9

1.1

2.4

{ "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 to the nearest tenth

Calculate the difference between the estimated values

Answer: