Simplify square root of square root of 256x^4

Problem

√(,√(,256*x^4))

Solution

1. Apply the property of nested radicals to combine the square roots into a single radical.

√(,√(,a))=√(4,a)

2. Rewrite the expression using a fourth root.

√(4,256*x^4)

3. Factor the constant inside the radical to see if it is a perfect fourth power.

256=4^4

4. Simplify the radical by taking the fourth root of each factor.

√(4,4^4⋅x^4)=4*|x|

Final Answer

√(,√(,256*x^4))=4*|x|

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