Question 64747
{{{sqrt(k+9)=sqrt(3)+sqrt(k)}}}
Square each side of the equation
{{{k+9=3+2*sqrt(3)*sqrt(k)+k}}}

{{{6=2*sqrt(3)*sqrt(k)}}}
Divide each side by 2
{{{3=sqrt(3)*sqrt(k)}}}
Divide each side by sqrt(3)
{{{sqrt(3)=sqrt(k)}}}
Square each side to get
3=k
Check in the original equation
{{{sqrt(3+9)=sqrt(3)+sqrt(3)}}}
{{{sqrt(12)=2sqrt(3)}}}
{{{sqrt(4*3)=2sqrt(3)}}}
{{{2sqrt(3)=2sqrt(3)}}}