If , sT = $\sqrt{\frac{[(a + T)T]}{a}}$ what does T equal?

Analyze the question: We must make T the subject of the formula. The way the question is typed, the "a" sits under the square root. That version gives an answer that is not among the options, so the question was probably garbled when copied. I'll show both readings.

As typed: sT = √[(a + T)T / a]

Square both sides: s²T² = (a + T)T / a

Divide by T: s²T = (a + T)/a

So as²T = a + T, which gives T(as² − 1) = a, and T = a / (as² − 1).

This is not among the options, so it is probably not what the examiners intended.

Likely intended version (the "a" is outside the root): sT = √[(a + T)T] / a

1. Multiply both sides by a: asT = √[(a + T)T]
2. Square both sides: a²s²T² = (a + T)T
3. Divide through by T (T ≠ 0): a²s²T = a + T
4. Collect the T terms: a²s²T − T = a
5. Factor out T: T(a²s² − 1) = a
6. Divide: T = a / (a²s² − 1)

This matches option D.

Exam tip: To make a variable the subject when it sits inside a square root, follow this order:

• Remove the root by squaring.
• Collect all terms containing the variable on one side.
• Factor the variable out.
• Divide to isolate it.

Also check the question carefully. A misplaced "a" changes the answer.