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Look over the roots that require absolute value.  Please summarize what you notice by writing a rule for when absolute value is needed.

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Look over the roots that require absolute value.  Please summarize what you notice by writing a rule for when absolute value is needed.

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when n is even and the radicand's degree is even, but the root's degree is odd, absolute value is needed

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When one side allows for an odd value (for the whole expression) while the other one only allows for non-negative values (for example, when the exponent is odd but the index is even)

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if the index and the exponent of the radicand are even, and the root's exponent is odd, the root needs Absolute Value. d

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when the index and radicand degree are matching with odd/even values, but the exponent to the other side is opposite to this, you will need absolute values

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When the side with the radical has all even exponents and index but the side it equals has odd exponents, then it must need absolute value.

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If the degree of the radicand is even, and the degree of the opposite side's quantity is odd the equation needs an absolute value

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If the degree of x is even inside the radical and the solution has an even degree too, then it is always true. If the degree of the radicand is different from the solution it needs an absolute value.

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When the degree of the radicand and and degree of the simplified form matches in terms of odd or even, it does not need an absolute value. If they do not match, an absolute value sign is needed. If the radicand is negative and simplified form is negative, no absolute value is needed. If they are both positive, no absolute value is needed. If they don't match, an absolute value sign is needed

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When n is even and the exponent is also even, then the simplified root does not need absolute value. This is also true if n is odd and the exponent is odd. However, if n is odd and the exponent is not the same, then the root needs absolute value.

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If the index and the exponent of the radicand are even and the exponent of the a on the other side of the equation is odd, then equation needs absolute value

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For n^rad(x^a*y^a...)=x^a/n, where a and n are non-negative integers, and x,y,etc are real varibles if a is even yet a/n is odd then you will need an absolute value.

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when the index is odd while the radicand's exponent is even, absolute value signs are needed.