recall that to simplify a square root, you can write the radicand as a product with factors that are perfect squares.

for example:
$\sqrt{108} = \sqrt{36 \cdot 3} = 6\sqrt{3}$

simplify: $\sqrt{240}$

$4\sqrt{15}$
$4 + \sqrt{15}$
$16\sqrt{15}$
$16 + \sqrt{15}$

Question

recall that to simplify a square root, you can write the radicand as a product with factors that are perfect squares.

for example:
$\sqrt{108} = \sqrt{36 \cdot 3} = 6\sqrt{3}$

simplify: $\sqrt{240}$

$4\sqrt{15}$
$4 + \sqrt{15}$
$16\sqrt{15}$
$16 + \sqrt{15}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Radical Simplification" ], "new_concepts": [], "current_concepts": [ "Radical Simplification" ] } ## Find the largest perfect square factor Using the *Radical Simplification* knowledge point $$ \begin{aligned} &240 = 16 \times 15\ &\text{where } 16 = 4^2 \text{ is a perfect square} \end{aligned} $$ ## Simplify the radical expression Using the *Radical Simplification* knowledge point $$ \begin{aligned} \sqrt{240} &= \sqrt{16 \cdot 15} \ &= \sqrt{16} \cdot \sqrt{15} \ &= 4\sqrt{15} \end{aligned} $$

(A) $4\sqrt{15}$

(B) $4 + \sqrt{15}$

(C) $16\sqrt{15}$

(D) $16 + \sqrt{15}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Radical Simplification" ] }

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QUESTION IMAGE

Question

Explanation:

Find the largest perfect square factor

Simplify the radical expression

Answer: