question 2

which of the following would result in an integer?

$\sqrt{51}$

$\sqrt{68}$

$\sqrt{25}$

$\sqrt{175}$

Question

question 2

which of the following would result in an integer?

$\sqrt{51}$

$\sqrt{68}$

$\sqrt{25}$

$\sqrt{175}$

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", "Perfect Squares", "Square Roots" ], "new_concepts": [], "current_concepts": [ "Number Classification", "Perfect Squares", "Square Roots" ] } ## Identify perfect squares among the radicands $$ \begin{aligned} 51 &\quad \text{is not a perfect square} \ 68 &\quad \text{is not a perfect square} \ 25 &= 5^2 \quad \text{is a perfect square} \ 175 &\quad \text{is not a perfect square} \end{aligned} $$ ## Evaluate the square roots $$ \begin{aligned} \sqrt{51} &\approx 7.14 otin \mathbb{Z} \ \sqrt{68} &\approx 8.25 otin \mathbb{Z} \ \sqrt{25} &= 5 \in \mathbb{Z} \ \sqrt{175} &\approx 13.23 otin \mathbb{Z} \end{aligned} $$ ## Determine the correct option $$ \sqrt{25} = 5 \quad (\text{an integer}) $$

(A) $\sqrt{51}$

(B) $\sqrt{68}$

(C) $\sqrt{25}$

(D) $\sqrt{175}$

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

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QUESTION IMAGE

Question

Explanation:

Identify perfect squares among the radicands

Evaluate the square roots

Determine the correct option

Answer: