Question 771119
3 times the square root of 44 plus 11 times the square root of 22 divided by square root of 33 minus the square root of 22
<pre>
{{{(3sqrt(44)+11sqrt(22))/(sqrt(33)-sqrt(22))}}}

The first term on top {{{3sqrt(44)=3sqrt(4*11)=3sqrt(4)sqrt(11)=3*2sqrt(11)=6sqrt(11)}}} 

{{{(6sqrt(11)+11sqrt(22))/(sqrt(33)-sqrt(22))}}}

Multiply by the conjugate of the denominator over itself:

{{{((6sqrt(11)+11sqrt(22))/(sqrt(33)-sqrt(22)))}}}{{{""*""}}}{{{((sqrt(33)+sqrt(22))/(sqrt(33)+sqrt(22)))}}}

{{{((6sqrt(11)+11sqrt(22))(sqrt(33)+sqrt(22)))/( sqrt(33)-sqrt(22))(sqrt(33)+sqrt(22) )}}}

{{{(6sqrt(11*33)+6sqrt(11*22)+11sqrt(22*33)+11*22)/(33-22)}}}

{{{(6sqrt(11*11*3)+6sqrt(11*11*2)+11sqrt(11*2*11*3)+11*22)/11}}}

{{{(6sqrt(11^2*3)+6sqrt(11^2*2)+11sqrt(11^2*6)+11*22)/11}}}

{{{(6*11sqrt(3)+6*11sqrt(2)+11*11sqrt(6)+11*22)/11}}}

{{{(11(6sqrt(3)+6sqrt(2)+11sqrt(6)+22))/11}}}

{{{(cross(11)(6sqrt(3)+6sqrt(2)+11sqrt(6)+22))/cross(11)}}}

6&#8730;<span style="text-decoration: overline">3</span> + 6&#8730;<span style="text-decoration: overline">2</span> + 11&#8730;<span style="text-decoration: overline">6</span> + 22

Edwin</pre>