which is an expression for $\sqrt{240}$ without a perfect square factor in the radicand?

a. $2\sqrt{60}$
b. $4\sqrt{30}$
c. $4\sqrt{15}$
d. $8\sqrt{30}$

Question

which is an expression for $\sqrt{240}$ without a perfect square factor in the radicand?

a. $2\sqrt{60}$
b. $4\sqrt{30}$
c. $4\sqrt{15}$
d. $8\sqrt{30}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Simplifying Radicals", "Radical Expressions" ], "current_concepts": [ "Simplifying Radicals", "Radical Expressions" ] } ## Find the largest perfect square factor of 240 $$ \begin{aligned} 240 &= 16 \times 15 \ 16 &= 4^2 \end{aligned} $$ ## Simplify the radical expression $$ \begin{aligned} \sqrt{240} &= \sqrt{16 \times 15} \ &= \sqrt{16} \times \sqrt{15} \ &= 4\sqrt{15} \end{aligned} $$ ## Verify the remaining radicand has no perfect square factors $$ \begin{aligned} 15 &= 3 \times 5 \end{aligned} $$

A. $2\sqrt{60}$

B. $4\sqrt{30}$

C. $4\sqrt{15}$

D. $8\sqrt{30}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Simplifying Radicals" ] }

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QUESTION IMAGE

Question

Explanation:

Find the largest perfect square factor of 240

Simplify the radical expression

Verify the remaining radicand has no perfect square factors

Answer: