nolan used the following procedure to find an estimate for $\sqrt{18}$.

step 1: since $4^2 = 16$ and $5^2 = 25$ and $16

Question

nolan used the following procedure to find an estimate for $\sqrt{18}$.

step 1: since $4^2 = 16$ and $5^2 = 25$ and $16 < 18 < 25$, $\sqrt{18}$ is between 4 and 5.
step 2: since 18 is closer to 16, square the tenths closer to 4.
$4.1^2 = 16.81$
$4.2^2 = 17.64$
$4.3^2 = 18.49$
$4.4^2 = 19.36$
step 3: since 18.49 rounds to 18, 4.3 is the best approximation for $\sqrt{18}$.

in which step, if any, did nolan make an error?

in step 1, $\sqrt{18}$ is between 4 and 5 because $\sqrt{18} \approx 20$ and $4 \times 5 = 20$.
in step 2, he made a calculation error when squaring.
in step 3, he should have determined which square is closest to 18.
nolan did not make an error.

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", "Iterative Approximation" ] } ## Analyze Nolan's steps for estimating $\sqrt{18}$ $$ \begin{aligned} &\text{Step 1: } 4^2 = 16,\ 5^2 = 25,\ 16 < 18 < 25 \implies 4 < \sqrt{18} < 5 \quad (\text{Correct})\ &\text{Step 2: } 4.1^2 = 16.81,\ 4.2^2 = 17.64,\ 4.3^2 = 18.49,\ 4.4^2 = 19.36 \quad (\text{Correct calculations})\ &\text{Step 3: } \text{Nolan states } 4.3 \text{ is the best approximation because } 18.49 \text{ rounds to } 18. \end{aligned} $$ ## Identify the error in Step 3 $$ \begin{aligned} &|17.64 - 18| = 0.36\ &|18.49 - 18| = 0.49\ &0.36 < 0.49 \implies 17.64 \text{ is closer to } 18 \text{ than } 18.49 \text{ is.}\ &\text{Therefore, } 4.2 \text{ is a better approximation than } 4.3. \end{aligned} $$ ## Match with the correct option $$ \text{Nolan should have determined which square is closest to } 18 \text{ instead of using rounding rules.} $$

(A) In step 1, $\sqrt{18}$ is between 4 and 5 because $\sqrt{18} \approx 20$ and $4 \times 5 = 20$.

(B) In step 2, he made a calculation error when squaring.

(C) In step 3, he should have determined which square is closest to 18.

(D) Nolan did not make an error.

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

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QUESTION IMAGE

Question

Explanation:

Analyze Nolan's steps for estimating \(\sqrt{18}\)

Identify the error in Step 3

Match with the correct option

Answer: