Question
Find the root. Assume that all variables represent nonnegative real numbers. sqrt[5]{x^{30}} Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. sqrt[5]{x^{30}}= B. The root is not a real number.
Ask by Hobbs Ford.
Mar 13,2025 22:32
UpStudy AI Solution
Tutor-Verified Answer
Answer
The root is \(x^6\).
Solution
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The Deep Dive
The expression \( \sqrt[5]{x^{30}} \) can be simplified using the property of exponents. Since \( \sqrt[5]{x^{30}} = x^{30/5} = x^6 \), and assuming \( x \) is a nonnegative real number, the root is simply \( x^6 \).
Now, if you consider any nonnegative real number for \( x \), \( x^6 \) will also be nonnegative, maintaining the real number condition. Thus, the root \( x^{30/5} \) is indeed a real number.
Feel free to plug in any value for \( x \) to see how it behaves—whether it’s 0, 1, or any positive number, the result will always be valid!
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