Math Problem Statement
Solution
The given problem asks to simplify the square root of 192 step by step.
To reduce , we need to factor 192 into its prime factors and find the perfect squares.
Step-by-Step Simplification:
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Start by finding the prime factorization of 192.
So, the prime factorization of 192 is:
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Group the factors into perfect squares where possible:
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Simplify the square root by taking out the perfect square:
Final Answer:
Would you like more details on any of the steps or further clarification?
Related Questions:
- How do you factor other square roots into prime factors?
- What is the method to handle cube roots or higher roots similarly?
- How do you simplify using prime factorization?
- What happens when the number inside the radical is already a perfect square?
- How can you break down cube roots using prime factorization?
Tip:
Always check if the number inside the square root has any perfect square factors, as this will help simplify the radical easily!
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Math Problem Analysis
Mathematical Concepts
Radicals
Prime Factorization
Formulas
\( \sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b} \)
Prime Factorization of 192: \( 192 = 2^6 \times 3 \)
Theorems
Square root of a product theorem
Suitable Grade Level
Grades 8-10