Make y the subject of the formula p=((x+y)/5)^(1/2)

To "make y the subject" basically means to get an expression in the form y= a function of the other variables (in this question, x and p). This will involve adding, subtracting, multiplying and dividing the expression by certain numbers and variables. This is fine to do as long as it is done to both sides of the expression, as this doesn't change the value of either side; it just makes it easier to manipulate. For example, x=y is exactly the same as 2x=2y; the value has not changed.

As in this expression, the most complicated part is the square root, it is best to adress this first so it doesn't cause any issues later on. To do this, square both sides; this gives the expression p^2=(x+y)/5. Next, it is logical to remove the 5 that x and y are divided by; to do this we multiply both sides by 5, and this gives us the expression 5(p^2)=x+y. This now makes it very easy to get an expression in the form y=; to do this, subtract x from both sides to give the final answer, y=5(p^2)-x=y.