Make q the subject of the relation t = √((pq/r) – r²q).

Explanation

We need to rearrange the equation to get q by itself on one side. Let’s work through it step by step.

Step 1: Square both sides to remove the square root.
t = √((pq/r) − r²q)
t² = (pq/r) − r²q

Step 2: Factor out q from the right side.
t² = q(p/r − r²)

Step 3: Simplify the bracket.
p/r − r² = p/r − r³/r = (p − r³)/r
So: t² = q × (p − r³)/r

Step 4: Solve for q.
Multiply both sides by r:
rt² = q(p − r³)
Divide both sides by (p − r³):
q = rt²/(p − r³)

The answer is q = rt²/(p − r³).