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

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phanpal999 | Student, Grade 8 | Salutatorian

Posted June 10, 2013 at 12:08 PM via web

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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 1) Educator Emeritus

Posted June 10, 2013 at 12:23 PM (Answer #1)

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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:

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

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

`=root(3)(a^3+b^2-b^2)`

`=root(3)(a^3)`

`=a`

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

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