Evaluate fifth root of 64

Problem

√(5,64)

Solution

1. Rewrite the number inside the radical as a power of a prime number.

√(5,2^6)

2. Apply the property of radicals √(n,a^m)=a^m/n to convert the expression into exponential form.

2^6/5

3. Decompose the fraction in the exponent into a whole number and a proper fraction to simplify the radical.

2^(1+1/5)

4. Use the product rule for exponents a^(m+n)=a^m⋅a^n to separate the terms.

2^1⋅2^1/5

5. Convert the fractional exponent back into radical form.

2√(5,2)

Final Answer

√(5,64)=2√(5,2)

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