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Home » $ B $ is a multiple of 11 - Crosslake

$ B $ is a multiple of 11 - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Rationalize the denominator of \( \frac{4}{\sqrt{5} - \sqrt{3}} \).

📌 To rationalize the denominator, multiply numerator and denominator by the conjugate \( \sqrt{5} + \sqrt{3} \):

📌 \frac{4}{\sqrt{5} - \sqrt{3}} \cdot \frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} + \sqrt{3}} = \frac{4(\sqrt{5} + \sqrt{3})}{(\sqrt{5})^2 - (\sqrt{3})^2} = \frac{4(\sqrt{5} + \sqrt{3})}{5 - 3} = \frac{4(\sqrt{5} + \sqrt{3})}{2} = 2(\sqrt{5} + \sqrt{3}).

📌 Thus, the rationalized expression is \( \boxed{2(\sqrt{5} + \sqrt{3})} \).

📌 Find the value of \( x \) that satisfies \( \log_2(x^2 - 4) = 3 \).

📌 Start by rewriting the logarithmic equation in exponential form:

📌 \[ \log_2(x^2 - 4) = 3 \Rightarrow x^2 - 4 = 2^3 = 8. \]

📌 Solve for \( x^2 \):

🔥 Popular Posts

Resuelve para \( x \) en la ecuación \( 3^{2x} = 81 \).
Reescribe 81 como \( 3^4 \).
Entonces, \( 3^{2x} = 3^4 \).
Igualando exponentes, \( 2x = 4 \).
Por lo tanto, \( x = 2 \).
Un tren viaja 150 millas a una velocidad de 50 mph, luego otras 200 mi...
Tiempo para la primera parte: \( \frac{150}{50} = 3 \) horas.
Tiempo para la segunda parte: \( \frac{200}{80} = 2.5 \) horas.
Distancia total: \( 150 + 200 = 350 \) millas.
Tiempo total: \( 3 + 2.5 = 5.5 \) horas.

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