Question 57204
{{{(x-2)*sqrt(x)=0}}}
By the zero product property {{{x-2=0}}} and {{{sqrt(x)=0}}}
{{{x-2+2=0+2}}}  and {{{(sqrt(x))^2=(0)^2}}}
{{{highlight(x=2)}}}   and {{{highlight(x=0)}}}
Check for extraneous solutions (false solutions):
for 2:
{{{(2-2)*sqrt(2)=0}}}
{{{0*sqrt(2)=0}}}
{{{0=0}}} 2 checks out.
for 0:
{{{(0-2)*sqrt(0)=0}}}
{{{-2*0=0}}}
{{{0=0}}} 0 checks out also.
Happy Calculating!!!