Question 697653
1. 

{{{(x-5)^(1/3)= 3^(1/2)}}}....both side raise to power of {{{3}}}

{{{(root(3,(x-5)))^3= (sqrt(3))^3}}}

{{{x-5= (sqrt(3))^2*sqrt(3)}}}

{{{x-5= 3*sqrt(3)}}}

{{{x= 3*1.73+5}}}

{{{x= 5.19+5}}}

{{{x= 10.19}}}



2.

{{{3/sqrt(x-3))=4/sqrt(2x+3)}}}......cross multiply

{{{3sqrt(2x+3)=4sqrt(x-3)}}}...both side raise to power of {{{2}}}

{{{3^2(sqrt(2x+3))^2=4^2(sqrt(x-3))^2}}}

{{{9(2x+3)=16(x-3)}}}

{{{18x+27=16x-48}}}

{{{18x-16x=-48-27}}}

{{{2x=-75}}}

{{{x=-75/2}}}

{{{x=-37.5}}}


3. 
{{{root(4,(2x-5))=sqrt(x+1)}}}....both side raise to power of {{{4}}}

{{{(root(4,(2x-5)))^4=(sqrt(x+1))^4}}}

{{{2x-5=(x+1)^2}}}

{{{2x-5=x^2+2x+1}}}

{{{-5-1=x^2+2x-2x}}}

{{{-6=x^2}}}

{{{sqrt(-6)=x}}}

{{{x=2.45i}}} or {{{x=-2.45i}}}