Math Problem Statement
Simplify \( \sqrt{54} \). Show all your work.
Solution
To simplify , we break it down step by step:
Step 1: Prime factorization of 54
The number can be factored into:
Step 2: Apply the square root
The square root of is:
We can split the square root as:
Step 3: Simplify perfect squares
Within , the part can be simplified:
Thus:
Final Answer:
Would you like further details or have additional questions?
Related Questions:
- What is the process to simplify square roots for larger numbers?
- Can you explain how to identify perfect squares within a number?
- What is the difference between simplifying and approximating square roots?
- How do you handle square roots of decimals?
- Can this approach be used for cube roots?
Tip: Always break numbers into prime factors when simplifying square roots—it reveals perfect squares easily!
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Math Problem Analysis
Mathematical Concepts
Simplification of square roots
Prime factorization
Properties of square roots
Formulas
\( \sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b} \)
\( \sqrt{n^2} = n \)
Theorems
Property of square roots (product rule)
Suitable Grade Level
Grades 6-8