which is the best estimate of $\sqrt{47}$ to the nearest tenth?

6.8
6.9
7.0
7.1

Question

which is the best estimate of $\sqrt{47}$ to the nearest tenth?

6.8
6.9
7.0
7.1

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", "Perfect Squares" ] } ## Identify bounding perfect squares $$ \begin{aligned} 36 &< 47 < 49 \ \sqrt{36} &< \sqrt{47} < \sqrt{49} \ 6 &< \sqrt{47} < 7 \end{aligned} $$ ## Evaluate squares of candidate values $$ \begin{aligned} 6.8^2 &= 46.24 \ 6.9^2 &= 47.61 \end{aligned} $$ ## Compare differences to find the closest estimate $$ \begin{aligned} |47 - 46.24| &= 0.76 \ |47 - 47.61| &= 0.61 \ 0.61 &< 0.76 \end{aligned} $$

(A) 6.8

(B) 6.9

(C) 7.0

(D) 7.1

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify bounding perfect squares

Evaluate squares of candidate values

Compare differences to find the closest estimate

Answer: