Question 881507
You will need to square both sides TWICE.


More than one way to solve, but here is maybe the easier way:


{{{sqrt(r)-6+sqrt(r+8)=6-6}}}
{{{sqrt(r)-6+sqrt(r+8)-sqrt(r+8)=0-sqrt(r+8)}}}
{{{sqrt(r)-6=-sqrt(r+8)}}}
Square both sides.
{{{r-2*6*sqrt(r)+36=r+8}}}
{{{-12sqrt(r)+36=8}}}
{{{-12sqrt(r)=8-36}}}
{{{-12sqrt(r)=-28}}}
Squ.................. not yet.
{{{sqrt(r)=-28/(-12)}}}
{{{sqrt(r)=7/3}}}

{{{highlight(r=49/9)}}}



CHECK:
{{{sqrt(r)+ sqrt(r+8)=6}}}
{{{sqrt(49/9)+sqrt(49/9+8)=6}}}
{{{7/3+sqrt((49+72)/9)=67/3+sqrt(121/9)=6}}}
{{{7/3+11/3=6}}}
{{{18/3=6}}} YES.