QQuestionMathematics
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
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