<PRE><B>Question 108372</B>
Simplify quotients containing radicals by rationalizing the denominator.
:
We multiply each expression by the denominator over itself (same as 1)
;
{{{30/sqrt(18)}}} * {{{sqrt(18)/sqrt(18)}}} = {{{30sqrt(18)/18}}}
:
We can extract a square:
{{{30sqrt(9*2)/18}}} = {{{30*3sqrt(2)/18}}} = {{{90sqrt(2)/18}}}
18 cancels into 90
{{{5sqrt(2)}}} is the simplified answer
:
:
{{{9/2sqrt(45)}}} * {{{sqrt(45)/sqrt(45)}}} = {{{9*sqrt(45)/2(45)}}} = {{{9*sqrt(9*5)/90}}} = {{{9*3sqrt(5)/90}}} = {{{27sqrt(5)/90}}}
:
Reduce the fraction divide by 9
{{{3sqrt(5)/10}}}
:
:
{{{3sqrt(6)/sqrt(2)}}} * {{{sqrt(2)/sqrt(2)}}} = {{{3sqrt(12)/2}}} = {{{3sqrt(4*3)/2}}} = {{{3*2sqrt(3)/2}}}
Cancel out 2:
{{{3sqrt(3)}}}</PRE>