Question
Find the real-number root. \( \sqrt[5]{32} \) Write your answer in simplified form.
Ask by Newton Coles. in Mexico
Mar 03,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The fifth root of 32 is 2.
Solution
To find the fifth root of 32, we need to solve for x in the equation x⁵ = 32.
Checking x = 2:
2⁵ = 2 × 2 × 2 × 2 × 2 = 32
Since 2⁵ equals 32, the fifth root of 32 is 2.
Thus, the simplified answer is 2.
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Simplify this solution The Deep Dive
The expression \( \sqrt[5]{32} \) can be simplified by recognizing that 32 can be expressed as \( 2^5 \). Therefore, we can rewrite the expression as: \[ \sqrt[5]{32} = \sqrt[5]{2^5} = 2^{5/5} = 2^1 = 2 \] So, the real-number root of \( \sqrt[5]{32} \) is \( 2 \).
