Make t the subject of k = $m \sqrt \frac{t-p}{r}$

Analyze the question: We need to rearrange k = m√((t − p)/r) so that t stands alone on one side.

Concept: To remove a square root, square both sides. Then use inverse operations to isolate t.

Solution:

1. Start with: k = m√((t − p)/r)

2. Divide both sides by m: k/m = √((t − p)/r)

3. Square both sides: k²/m² = (t − p)/r

4. Multiply both sides by r: k²r/m² = t − p

5. Add p to both sides: t = k²r/m² + p

6. Combine over a common denominator: t = (k²r + pm²)/m²

Matching to the options: This is exactly option B, (k²r + pm²)/m².

Check the others:

• A, (k²r + p)/m², would be wrong because p was not multiplied by m² when combining the fractions.
• C has the wrong sign and the same missing m².
• D uses p² instead of pm², which has no basis in the working.

Tip: When you have a "subject of the formula" question with a square root, always follow this order: isolate the root, square both sides, then clear the fractions. When you add a plain term like p to a fraction with denominator m², remember to multiply it by m² to get a common denominator. That is where many students lose marks.