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Q
QuestionMathematics

"Select the correct answer. What is 192 in simplest form? A. 32√3 ​B. 3√8 ​C. 8√3 ​D. 2√48"
12 months agoReport content

Answer

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Step 1:
Let's solve this step by step:

Step 2:
: Simplify 192 by finding its prime factorization

192 = 2^{6} \times 3^{1}

Step 3:
: Rewrite 192 as a product of a perfect square and a square-free number

• Remaining factor is $$2^{0} \times 3^{1} = 3
• We want to pull out the largest perfect square factor

Step 4:
: Rewrite the expression

192 = 8^{2} \times 3 = 64 \times 3 = 8\sqrt{3}

Step 5:
: Check the given options

Looking at the choices, $$8\sqrt{3}$$ matches option C.

Final Answer

Key insights: • Prime factorization helps simplify radical expressions • Look for the largest perfect square factor • Simplify by separating perfect square and remaining radical components