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

$4/3sqrt2$

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