Question 407910
{{{((sqrt(10)+2sqrt(5)))/((sqrt(10)+sqrt(5)))}}}
<pre><font face = "batangche" color = "indigo" size = 4><b>

The conjugate of the denominator is {{{red((sqrt(10)-sqrt(5)))}}}.
Put that over itself like this {{{(red((sqrt(10)-sqrt(5))))/red((sqrt(10)-sqrt(5)))}}}.

Then multiply:

{{{

expr((sqrt(10)+2sqrt(5))*red((sqrt(10)-sqrt(5))))/
expr((sqrt(10)+sqrt(5))*red((sqrt(10)-sqrt(5)))) )}}}

Multiply the tops and the bottoms:

{{{
(sqrt(100)-sqrt(50)+2sqrt(50)-2sqrt(25))/
(sqrt(100)-sqrt(50)+sqrt(50)-sqrt(25)) }}}

Simplify:

{{{
(sqrt(100)-sqrt(50)+2sqrt(50)-2sqrt(25))/
(sqrt(100)-cross(sqrt(50))+cross(sqrt(50))-sqrt(25)) }}}

{{{
(sqrt(100)+sqrt(50)-2sqrt(25))/
(sqrt(100)-sqrt(25)) }}}

{{{
(10+sqrt(50)-2*5)/
(10-5) }}}

{{{
(10+sqrt(50)-10)/
5 }}}

{{{
(cross(10)+sqrt(50)-cross(10))/
5 }}}

{{{
(sqrt(50))/
5 }}}

{{{
(sqrt(25*2))/
5 }}}

{{{
(sqrt(25)sqrt(2))/5 }}}

{{{
(5sqrt(2))/5 }}}

{{{
(cross(5)sqrt(2))/cross(5) }}}

{{{sqrt(2)}}}

Edwin</pre>