JAMB - Mathematics (2025 - No. 46)

\(\sqrt{75} - \sqrt{12} + \sqrt{27} = y\sqrt{3}\)

Simplify each term:

- \(\sqrt{75} = \sqrt{25 \times 3} = 5\sqrt{3}\)
- \(\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}\)
- \(\sqrt{27} = \sqrt{9 \times 3} = 3\sqrt{3}\)

Substitute: \(5\sqrt{3} - 2\sqrt{3} + 3\sqrt{3} = y\sqrt{3}\)

Combine like terms: \((5 - 2 + 3)\sqrt{3} = y\sqrt{3}\)

\(6\sqrt{3} = y\sqrt{3}\)

Thus, y = 6