Simplify square root of 1-(x^2)^2

Problem

√(,1−(x2)2)

Solution

1. Apply the power rule for exponents to the inner term (x2)2

√(,1−x(2⋅2))

2. Multiply the exponents to simplify the expression inside the radicand.

√(,1−x4)

3. Identify if further simplification is possible. While 1−x4 is a difference of squares that factors into (1−x2)*(1+x2) it does not result in a perfect square that can be removed from the square root.

Final Answer

√(,1−(x2)2)=√(,1−x4)

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