Simplify `(root(3)(sqrt(a^3+b^2)+b)))*(root(3)(sqrt(a^3+b^2)-b))`

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embizze | High School Teacher | (Level 2) Educator Emeritus

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Simplify `root(3)(sqrt(a^3+b^2)+b)*root(3)(sqrt(a^3+b^2)-b)`

First use `root(3)(m)*root(3)(n)=root(3)(mn)` to rewrite as:


Now multiply the binomial -- recall that `sqrt(m)sqrt(m)=m`; also note that this is the difference of two squares :







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