What is the fourth square root of 81?
Understand the Problem
The question is asking for the fourth root of 81, which involves finding a number that, when raised to the power of 4, equals 81. This requires understanding of exponents and roots.
Answer
The fourth root of 81 is $3$.
Answer for screen readers
The fourth root of 81 is $3$.
Steps to Solve
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Identify the root to calculate We need to find the fourth root of 81, which can be expressed mathematically as $x = 81^{1/4}$.
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Rewrite the exponent To compute $81^{1/4}$, it helps to express 81 as a power of another number. We note that $81 = 3^4$. Therefore, we can rewrite the expression as: $$ x = (3^4)^{1/4} $$
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Simplify the exponent Using the property of exponents, where $(a^m)^n = a^{m \cdot n}$, we simplify the equation: $$ x = 3^{4 \cdot \frac{1}{4}} = 3^1 $$
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Calculate the final value Finally, we evaluate $3^1$: $$ x = 3 $$
The fourth root of 81 is $3$.
More Information
Finding roots and understanding exponents are fundamental concepts in mathematics. Roots are often used in various practical applications, and recognizing numbers as powers of other integers can simplify calculations.
Tips
- Misidentifying the base: Always double-check the prime factorization of numbers like 81. It is easy to miscalculate or overlook.
- Forgetting the root property: Remember that when simplifying roots, you can convert the base of an exponent using multiplication of the exponents.
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