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Home » Bottle Flipping Game: Watch These Mind-Blowing Flip Secrets Go Viral! - Coaching Toolbox

Bottle Flipping Game: Watch These Mind-Blowing Flip Secrets Go Viral! - Coaching Toolbox

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 Final answer: $ \boxed{30 - 12\sqrt{6}} $

📌 Question: Rationalize the denominator of $ \frac{5}{\sqrt{7} + \sqrt{2}} $.

📌 Multiply numerator and denominator by the conjugate $ \sqrt{7} - \sqrt{2} $:

📌 \frac{5}{\sqrt{7} + \sqrt{2}} \cdot \frac{\sqrt{7} - \sqrt{2}}{\sqrt{7} - \sqrt{2}} = \frac{5(\sqrt{7} - \sqrt{2})}{(\sqrt{7} + \sqrt{2})(\sqrt{7} - \sqrt{2})}

📌 Simplify the denominator using the difference of squares:

📌 \frac{5(\sqrt{7} - \sqrt{2})}{5} = \sqrt{7} - \sqrt{2}

📌 Final answer: $ \boxed{\sqrt{7} - \sqrt{2}} $

📌 Question: Expand the product $ (x^2 + 2x + 3)(x^2 - 2x + 3) $.

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