Evaluate fifth root of 32

Problem

√(5,32)

Solution

1. Identify the number whose fifth power equals the radicand, 32.

2. Rewrite the number 32 as a power of its smallest prime factor, which is 2.

3. Calculate the prime factorization: 2×2×2×2×2=32

4. Substitute the exponential form into the radical: √(5,2)

5. Simplify the expression by applying the property √(n,an)=a for positive a

Final Answer

√(5,32)=2

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