Evaluate fourth root of 256

Problem

√(4,256)

Solution

1. Identify the operation as finding a number that, when multiplied by itself four times, equals 256

2. Rewrite the number 256 as a power of a smaller prime base to simplify the root.

3. Factor the number 256 by dividing by 2 repeatedly: 256=2

4. Apply the property of radicals where √(n,xm)=x(m/n)

5. Substitute the values into the property: 256(1/4)=(2)(1/4)

6. Simplify the exponent by multiplying 8 and 1/4 2(8/4)=2

7. Calculate the final value: 2=4

Final Answer

√(4,256)=4

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