This is your error "(a^2+ b^2)^{1/2}" is NOT (a^2)^{1/2}+ (b^2)^{1/2}

Instead square both sides of 25= (49+ y^2)^{1/2} to get 625= 49+ y^2, y^2= 625- 49= 576.

18= y which is incorrect

The math lab says this is the correct answer Y=-24 but i get something different. Can anyone help me solve this or explain where i went wrong.