Evaluate - fourth root of 256

Problem

√(4,256)

Solution

1. Identify the number whose fourth power equals the radicand, 256.

2. Factor the number 256 into its prime factors to see the powers of 2.

256=2⋅128

256=2⋅2⋅64

256=2⋅2⋅2⋅32

256=2⋅2⋅2⋅2⋅16

256=2⋅2⋅2⋅2⋅2⋅2⋅2⋅2

3. Group the factors into four equal sets to find the fourth root.

256=2

256=(2)4

256=4

4. Apply the definition of the principal nth root, where √(n,xn)=x for x≥0

√(4,4)=4

Final Answer

√(4,256)=4

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