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Calculate E = ((-`sqrt8` + `sqrt18` )/`sqrt2`  + `root(3)(24/27)` + `root(3)3` /3 - 1)^3

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lixalixa | Honors

Posted July 9, 2013 at 5:39 PM via web

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Calculate E = ((-`sqrt8` + `sqrt18` )/`sqrt2`  + `root(3)(24/27)` + `root(3)3` /3 - 1)^3

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted July 9, 2013 at 5:49 PM (Answer #1)

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You need to perform the following radical operations, such that:

`sqrt 8 = sqrt(2^3) => sqrt 8 = 2sqrt 2`

`sqrt 18 = sqrt(2*9) => sqrt18 = 3sqrt2`

`root(3)24 = root(3)(8*3) = 2root(3)3`

`root(3)27 = root(3)(3^3) => root(3)27 = 3`

Re-writing the expression, yields:

`E = ((-2sqrt 2 + 3sqrt2)/sqrt 2 + (2root(3)3)/3 + (root(3)3)/3 - 1)^3`

`E = (sqrt2/sqrt2 + (3root(3)3)/3 - 1)^3`

Reducing duplicte factors yields:

`E = (1 + (root(3)3) - 1)^3`

Reducing duplicate members yields:

`E = ((root(3)3))^3 => E = 3`

Hence, performing the indicated operations in the expression that contains radicals, yields `E = 3.`

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