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Home » B. The amplitude of the reflected wave - Dachbleche24

B. The amplitude of the reflected wave - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 5Question: Rationalize the denominator of $\displaystyle rac{3}{\sqrt{7} - \sqrt{2}}$ and simplify.

📌 Solution: To rationalize the denominator, multiply numerator and denominator by the conjugate $\sqrt{7} + \sqrt{2}$:

📌 rac{3}{\sqrt{7} - \sqrt{2}} \cdot rac{\sqrt{7} + \sqrt{2}}{\sqrt{7} + \sqrt{2}} = rac{3(\sqrt{7} + \sqrt{2})}{(\sqrt{7} - \sqrt{2})(\sqrt{7} + \sqrt{2})}

📌 Using the difference of squares in the denominator:

📌 rac{3(\sqrt{7} + \sqrt{2})}{5} = rac{3\sqrt{7} + 3\sqrt{2}}{5}

📌 Final simplified form:

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