Math Problem Statement
Simplify. Assume a is greater than or equal to zero. \( \sqrt{18a^5} \)
Solution
The given expression is:
We are asked to simplify this expression, assuming .
Step-by-step simplification:
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Factor the radicand: We can simplify . Since , we have:
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Simplify : We break into , where is a perfect square:
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Combine the results: Now, substituting back into the original expression: This simplifies to:
Thus, the simplified expression is:
Would you like any further details or clarification?
Related Questions:
- How do you simplify square roots involving both constants and variables?
- What is the process for factoring numbers under a square root?
- How does the assumption affect the solution?
- Can this expression be further simplified if we know specific values for ?
- How does the exponent rule apply to square roots?
Tip:
Always look for perfect squares when simplifying square roots—they can greatly reduce the complexity of the expression.
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Math Problem Analysis
Mathematical Concepts
Simplification
Square Roots
Exponents
Radical Expressions
Formulas
√(x * y) = √x * √y
√(a^n) = a^(n/2)
Theorems
Product Rule of Radicals
Exponent Rules
Suitable Grade Level
Grades 9-11