https://r2.erweima.ai/mathbot/image/1725449824955s9m7enbu.jpg

Let's analyze the questions in the image:

### a) Eliminar la raíz cuadrada \( \sqrt{3} + \sqrt{5} = 2 \)
This part likely requires simplifying or rationalizing the equation, but it seems to have a mistake since \( \sqrt{3} + \sqrt{5} \neq 2 \). You might need to clarify this or perhaps there's a context where this is true under certain conditions.

### b) Racionalizar la fracción (sqrt(5) + sqrt(2)) / (sqrt(7) - sqrt(2))
This question asks to rationalize the denominator of the given fraction. Rationalizing involves multiplying the numerator and denominator by the conjugate of the denominator.

### c) ¿Cuál es la PMDC de 315 y 525?
This asks for the "PMDC" (which likely means "Máximo Divisor Común", or GCD in English) of 315 and 525. The GCD is the greatest number that divides both numbers without leaving a remainder.

### d) Resuelve la ecuación cúbica con respecto a x: \( x^3 - 5x^2 - 2x + 8 = 0 \)
This is a cubic equation that needs to be solved for \( x \).

### e) Jorge a 50 km de la casa de Sebastián. Después de 2 horas, Jorge está a 30 km de la casa de Sebastián. ¿Cuál es la velocidad de Jorge?
This asks for the speed of Jorge, based on the distance and time given.

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### Let's work on each of these questions:

### a) Simplification of \( \sqrt{3} + \sqrt{5}

Elimina la raíz cuadrada √3 + √5 = 2; Racionaliza la fracción (√5 + √2) / (√7 - √2); ¿Cuál es la PMDC de 315 y 525?; Resuelve la ecuación cúbica con respecto a x: x³ - 5x² - 2x + 8 = 0; Jorge está a 50 km de la casa de Sebastián. Después de 2 horas, Jorge está a 30 km de la casa de Sebastián. ¿Cuál es la velocidad de Jorge?

Learn how to solve various mathematical problems, including simplifying square roots, rationalizing fractions, finding the Greatest Common Divisor (GCD), solving cubic equations, and calculating speed. This page provides detailed step-by-step solutions suitable for students in Grades 9-12.

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