How do you rationalize the denominator and simplify $root3( (1 / (2x^2)))$ ?

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Answer 1 · 2017-08-20T19:16:16

You $ul("force")$ it into something you can take the cube root of.

$=root(3)(4x)/(2x)$

Multiply by 1 and you do not change the intrinsic value. However, 1 comes in many forms

$color(green)(root(3)(1/(2x^2)color(red)(xx1)))$

$2xx2^2=2^3$

$x^2xx x^2xx x^2 =x^2xx(x^2)^2 = (x^2)^3$

$color(green)(root(3)(1/(2x^2)color(red)(xx(2^2(x^2)^2)/(2^2(x^2)^2))))" "->" "root(3)((4x^4)/(2^3(x^2)^3))$

$color(white)("vvvvvvvvvvvvvvv")->" "root(3)(4x^4)/(2x^2)$
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Simplified further

$x^4->x^3xx x" "$ so we can change the $4x^4$ such that we have:

$(xroot(3)4x)/(2x^2) = x/x xxroot(3)(4x)/(2x)$

$=root(3)(4x)/(2x)$

How do you rationalize the denominator and simplify root3( (1 / (2x^2)))root3( (1 / (2x^2)))?