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)

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

2

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)=am⋅an to separate the terms.

2⋅2

5. Convert the fractional exponent back into radical form.

2√(5,2)

Final Answer

√(5,64)=2√(5,2)

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