what is the sum and classification of $\frac{3}{20} + \sqrt{10}$?

$3.31227766...,$ irrational
$3.31227766...,$ rational
$18.16227766...,$ irrational
$18.16227766...,$ rational

Question

what is the sum and classification of $\frac{3}{20} + \sqrt{10}$?

$3.31227766...,$ irrational
$3.31227766...,$ rational
$18.16227766...,$ irrational
$18.16227766...,$ rational

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Number Classification", "Irrational Numbers" ], "new_concepts": [], "current_concepts": [ "Number Classification", "Irrational Numbers", "Decimal Expansion" ] } ## Evaluate the terms $$ \begin{aligned} \frac{3}{20} &= 0.15 \ \sqrt{10} &\approx 3.16227766... \end{aligned} $$ ## Calculate the sum $$ \begin{aligned} \text{Sum} &= 0.15 + 3.16227766... \ &= 3.31227766... \end{aligned} $$ ## Classify the sum $$ \begin{aligned} &\text{Rational} + \text{Irrational} = \text{Irrational} \ &\text{Sum is irrational} \end{aligned} $$

(A) 3.31227766..., irrational

(B) 3.31227766..., rational

(C) 18.16227766..., irrational

(D) 18.16227766..., rational

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Number Theory", "Irrational Numbers" ] }

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Question

Explanation:

Evaluate the terms

Calculate the sum

Classify the sum

Answer: