Question 228591
1) {{{z*sqrt(80zu^2) - u*sqrt(5z^3)}}}
Factor to reveal the perfect squares
{{{z*sqrt(16*5*z*u^2) - u*sqrt(5*z^2*z)}}}
extract the squares and combine like terms
{{{4uz*sqrt(5z) - uz*sqrt(5z)}}} = {{{3uz*sqrt(5z)}}}
;
;
2) {{{sqrt(z+16) = sqrt(7z+12)}}}
Square both sides:
z + 16 = 7z + 12
16 - 12 = 7z - z
4 = 6z
z = {{{4/6}}} = {{{2/3}}}
;
;
3) {{{sqrt(-6w+16) = w}}}
square both sides
-6w + 16 = w^2
0 = w^2 + 6w - 16
Factors to:
(w+8)(w-2) = 0
Two solutions
w = -8
w = +2; 
Check both solutions in the original equation (only one is valid)
:
:
4) {{{sqrt(10+8)/(-5*sqrt(10+1))}}} = {{{sqrt(18)/(-5*sqrt(11))}}} = {{{sqrt(9*2)/(-5*sqrt(11))}}} = {{{-3*sqrt(2)/(5*sqrt(11))}}}