which number is farthest from 2 on the number line?

$\sqrt{2.1}$
$\sqrt{2.4}$
$\sqrt{2.5}$
$\sqrt{2.9}$

Question

which number is farthest from 2 on the number line?

$\sqrt{2.1}$
$\sqrt{2.4}$
$\sqrt{2.5}$
$\sqrt{2.9}$

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" ] } ## Express the reference number as a square root $$ 2 = \sqrt{4} $$ ## Compare the values under the square root $$ \begin{aligned} |4 - 2.1| &= 1.9 \ |4 - 2.4| &= 1.6 \ |4 - 2.5| &= 1.5 \ |4 - 2.9| &= 1.1 \end{aligned} $$ ## Determine the farthest value $$ \text{Since } 1.9 > 1.6 > 1.5 > 1.1\text{, the value } \sqrt{2.1} \text{ is farthest from } \sqrt{4} \text{ on the number line.} $$

(A) $\sqrt{2.1}$

(B) $\sqrt{2.4}$

(C) $\sqrt{2.5}$

(D) $\sqrt{2.9}$

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

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QUESTION IMAGE

Question

Explanation:

Express the reference number as a square root

Compare the values under the square root

Determine the farthest value

Answer: