Evaluate fourth root of 64

Problem

√(4,64)

Solution

1. Rewrite the number inside the radical as a power of a prime number to make it easier to simplify.

64=2

2. Apply the property of radicals that states √(n,xm)=xm/n

√(4,2)=2

3. Simplify the fraction in the exponent by dividing both the numerator and the denominator by their greatest common divisor, which is 2.

6/4=3/2

4. Convert the expression back into radical form.

2=√(,2)

5. Simplify the square root by factoring out perfect squares.

√(,2)=√(,2⋅2)

√(,2⋅2)=2√(,2)

Final Answer

√(4,64)=2√(,2)

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