Math Problem Statement
Simplify \( \sqrt{9x^{13}} \) assuming that the variable represents a positive real number.
Solution
The expression you provided is:
We need to simplify this under the assumption that is a positive real number.
Step-by-step simplification:
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Factor the expression inside the square root:
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Simplify :
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Simplify : Use the property of square roots: . So,
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Combine the results:
Thus, the simplified expression is:
Would you like more details, or do you have any questions on how this was done?
Relative questions:
- What is the rule for simplifying square roots of powers, and why does become ?
- Can you explain why equals 3?
- How would the answer change if were a negative number?
- How can this simplification be used in solving equations or practical applications?
- What is the difference between simplifying expressions and solving equations?
Tip:
When simplifying square roots involving exponents, always remember to halve the exponent of any variable under the radical.
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Math Problem Analysis
Mathematical Concepts
Simplification
Square Roots
Exponents
Radicals
Formulas
\( \sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b} \)
\( \sqrt{x^a} = x^{a/2} \)
Theorems
Properties of Exponents
Properties of Square Roots
Suitable Grade Level
Grades 9-12