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

Problem

√(,1−(x^2)^2)

Solution

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

√(,1−x^(2⋅2))

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

√(,1−x^4)

3. Identify if further simplification is possible. While 1−x^4 is a difference of squares that factors into (1−x^2)*(1+x^2) it does not result in a perfect square that can be removed from the square root.

Final Answer

√(,1−(x^2)^2)=√(,1−x^4)

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