Math Problem Statement
Simplify the expression \(\sqrt{81 y^{21}}\), assuming y represents a positive real number.
Solution
The expression provided is:
We are asked to simplify this expression, assuming is a positive real number.
Step-by-Step Simplification:
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Rewrite the square root:
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Simplify the square root of 81:
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Simplify the square root of : Using the property , we can simplify:
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Final Simplified Expression:
Thus, the simplified form is:
Would you like further details on any step, or do you have any additional questions?
Related Questions:
- How do you simplify expressions involving higher roots?
- What happens if is not a positive real number in this case?
- Can you express using radicals instead of exponents?
- How do you handle fractional exponents in algebraic expressions?
- What if the base were not a perfect square, how would you simplify the expression?
Tip:
When simplifying square roots, it's useful to remember that fractional exponents can often make the process more straightforward.
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Math Problem Analysis
Mathematical Concepts
Algebra
Radicals
Exponents
Formulas
\( \sqrt{a^n} = a^{n/2} \)
\( \sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b} \)
Theorems
Exponent Rules
Square Root Properties
Suitable Grade Level
Grades 9-11