If `s = t + sqrt((r^(3))/(q))`, what is the value of r in terms of q, s and t ?

Options

A. `root(3)(qs^(2)-qt)`
B. `root(3)((s^(2)-2st-t^(2))/(q))`
C. `root(3)(qs^(2)-2qst+qt^(2))`
D. `sqrt((qs^(2)+2qst-t^(2))/(3))`

Answer

C

Explanation

Your goal is to get an equation with just the variable r on one side. The first variable you should move is t. Subtract it from both sides :
`s-t = sqrt((r^(3))/(q))`
Next, get rid of the radical sign on the left side by squaring both sides :
`(s-t)^(2)=(sqrt((r^(3))/(q)))^(2)`
`s^(2)-2st+t^(2)=(r^(3))/(q)`
You can get rid of the denominator on the right side of the equation by multiplying both sides by q :
`q(s^(2)-2st+t^(2))=q((r^(3))/(q))`
`qs^(2)-2qst+qt^(2)=r^(3)`
Finally, to get r alone on the right side, take tha cube root of each each side :
`root(3)(qs^(2)-2qst+qt^(2))=root(3)(r^(3))`
`root(3)(qs^(2)-2qst)+qt^(2)=r`