If y = $\frac{(2\sqrt{x^2 + m})}{3N}$, make x the subject of the formular

Analyze the question: We need to make x the subject of y = 2√(x² + m) / (3N).

Concept: To free x from a square root, isolate the root, square both sides, then solve for x².

Solution:

1. Multiply both sides by 3N: 3Ny = 2√(x² + m)

2. Divide by 2: √(x² + m) = 3Ny/2

3. Square both sides: x² + m = 9N²y²/4

4. Make x² the subject: x² = 9N²y²/4 − m = (9N²y² − 4m)/4

5. Take the square root: x = √(9y²N² − 4m) / 2

Matching the options: This is exactly option B.

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Tip: When you see a square root in a "change of subject" question, follow this order: isolate the root, square both sides, then solve. Remember to square the whole side, including the denominator: (3Ny/2)² = 9N²y²/4, not 9N²y²/2.