Simplify square root of square root of 16x^4

Problem

√(,√(,16*x4))

Solution

1. Simplify the inner radical by taking the square root of the expression 16*x4

√(,16*x4)=4*x2

2. Substitute the result back into the outer radical.

√(,4*x2)

3. Simplify the outer radical by taking the square root of 4*x2

√(,4*x2)=2*|x|

4. Note the absolute value because the square root of a squared variable must be non-negative. If x is assumed to be non-negative, it simplifies to 2*x

Final Answer

√(,√(,16*x4))=2*|x|

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