EKURHULENI WEST TVET COLLEGE \( 2.2 \quad \frac{\sqrt{75}+\sqrt{12}-\sqrt{108}}{\sqrt{147}} \) 2.2 Rationalize th
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To simplify \( \frac{\sqrt{75}+\sqrt{12}-\sqrt{108}}{\sqrt{147}} \), we start by simplifying under the square roots. \( \sqrt{75} = 5\sqrt{3} \), \( \sqrt{12} = 2\sqrt{3} \), and \( \sqrt{108} = 6\sqrt{3} \). Substituting these values gives us \( \frac{5\sqrt{3} + 2\sqrt{3} - 6\sqrt{3}}{\sqrt{147}} = \frac{(5 + 2 - 6)\sqrt{3}}{\sqrt{147}} = \frac{1\sqrt{3}}{\sqrt{147}} \). Next, we simplify the denominator: \( \sqrt{147} = \sqrt{49 \times 3} = 7\sqrt{3} \). Thus, we have \( \frac{\sqrt{3}}{7\sqrt{3}} \) which simplifies to \( \frac{1}{7} \). To rationalize the solution \( \frac{1}{7} \), we can multiply the numerator and denominator by 7. However, since it is already in the simplest fractional form, the final simplified result is simply \( \frac{1}{7} \).
