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📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 The solutions are $ \boxed{2 + \sqrt{7}} $ and $ \boxed{2 - \sqrt{7}} $.

📌 Question: Rationalize the denominator of $ \frac{\sqrt{5}}{\sqrt{3} - \sqrt{2}} $.

📌 Solution: Multiply numerator and denominator by $ \sqrt{3} + \sqrt{2} $:

📌 $$ \frac{\sqrt{5}(\sqrt{3} + \sqrt{2})}{(\sqrt{3} - \sqrt{2})(\sqrt{3} + \sqrt{2})} $$

📌 Simplify denominator:

📌 $$ (\sqrt{3})^2 - (\sqrt{2})^2 = 3 - 2 = 1 $$

📌 Thus, the expression becomes:

📌 $$ \sqrt{5}(\sqrt{3} + \sqrt{2}) = \sqrt{15} + \sqrt{10} $$

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