Question 710988
Solve by squaring your equation
(1) {{{sqrt(y)}}} + {{{sqrt(y + 5)}}} = 5 and get
(2) y + 2*{{{sqrt(y)}}}*{{{sqrt(y+5)}}} + (y+5) = 25 or
(3) {{{sqrt(y)}}}*{{{sqrt(y+5)}}} = 10 - y
Now square (3) to get
(4) y*(y + 5) = 100 -20y + {{{y^2}}} or
(5) {{{y^2}}} + 5y = {{{y^2}}} -20y + 100 or
(6) 5y = -20y + 100 or
(7) 25y = 100 or
(8) y = 4
Let's check your answer in (1)
Is ({{{sqrt(4)}}} + {{{sqrt(4 + 5)}}} = 5)?
Is (2 + {{{sqrt(9)}}} = 5)?
Is (2 + 3 = 5)?
Is (5 = 5)? Yes
Answer: y = 4