How do you simplify $(root3(10))/(root3(32))$ ?

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Answer 1 · 2017-08-24T18:35:41

See a solution process below:

First, we can rewrite the expression as:

$root(3)(10)/root(3)(8 * 4) => root(3)(10)/(root(3)(8)root(3)(4)) => root(3)(10)/(2root(3)(4))$

Next, we can rationalize the fraction by multiplying by the appropriate form of $1$ :

$root(3)(2)/root(3)(2) xx root(3)(10)/(2root(3)(4)) =>$

$(root(3)(2)xx root(3)(10))/(2root(3)(4) xx root(3)(2)) =>$

$root(3)(2 xx 10)/(2root(3)(4 xx 2)) =>$

$root(3)(20)/(2root(3)(8)) =>$

$root(3)(20)/(2 xx 2)$

$root(3)(20)/4$

How do you simplify (root3(10))/(root3(32))(root3(10))/(root3(32))?