Rational and Radical Equations
Aligned to A-REI.A.2 — Common Core State Standards for Mathematics.
What this lesson teaches
Solve rational equations by clearing denominators and radical equations by isolating the root and squaring. Because these steps can introduce false solutions, always check each answer in the original equation.
Worked example
Solve √(x + 2) = x. Squaring gives x + 2 = x^2, so x^2 − x − 2 = 0, which factors as (x − 2)(x + 1) = 0, giving x = 2 or x = −1. Checking: √4 = 2 works, but √1 = 1 ≠ −1, so x = −1 is extraneous and only x = 2 is valid.
Practice questions
- Solve √x = 5.
- Solve √(2x − 1) = 3.
- Solve √(x + 6) = x and identify any extraneous solution.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Ecuaciones racionales y con radicales
Resuelve ecuaciones racionales eliminando denominadores y ecuaciones con radicales aislando la raíz y elevando al cuadrado. Como estos pasos pueden introducir soluciones falsas, siempre verifica cada respuesta en la ecuación original.
Ejemplo: Resuelve √(x + 2) = x. Al elevar al cuadrado se obtiene x + 2 = x^2, así que x^2 − x − 2 = 0, que se factoriza como (x − 2)(x + 1) = 0, dando x = 2 o x = −1. Al verificar: √4 = 2 funciona, pero √1 = 1 ≠ −1, así que x = −1 es extraña y solo x = 2 es válida.
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