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Rationalize: 1/³√4 - 2Please show solution and explain

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spock7 | Student, Undergraduate | Honors

Posted May 3, 2012 at 5:16 PM via web

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Rationalize: 1/³√4 - 2

Please show solution and explain

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted May 3, 2012 at 5:24 PM (Answer #1)

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You need to remove the radical from denominator, hence, you should multiply by `(root(3)(16) + 2root(3)(4) + 4)`  such that:

`(root(3)(16) + 2root(3)(4) + 4)/((root(3)(4) - 2)(root(3)(16) + 2root(3)(4) + 4)) = (root(3)(16) + 2root(3)(4) + 4)/(4 - 8)`

`1/(root(3)(4) - 2) = (root(3)(16) + 2root(3)(4) + 4)/(-4)`

Hence, rationalizing the fraction yields `1/(root(3)(4) - 2) = (root(3)(16) + 2root(3)(4) + 4)/(-4).`

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