What is the simplest radical form of #(4sqrt(90)) /( 3sqrt(18))#?

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Answer 1 · 2018-04-06T02:09:42

#4/3sqrt2#

We should simplify each root individually.

#sqrt90=sqrt(9*10)#

Recall that #sqrt(a*b)=sqrtasqrtb,# so

#sqrt(9*10)=sqrt3sqrt10=3sqrt10#

Now,

#sqrt18=sqrt(9*2)=sqrt9sqrt2=3sqrt2#

Thus, we have

#(4(3)sqrt10)/(3(3)sqrt2)=(12sqrt10)/(9sqrt2)#

Recalling that #sqrta/sqrtb=sqrt(a/b), sqrt(10)/sqrt2=sqrt(10/2)=sqrt5#

Moreover, #12/9=4/3.#

So, the simplest form is

#4/3sqrt2#