Radical and Rational Equations
Aligned to A-REI.A.2 — Common Core State Standards for Mathematics.
What this lesson teaches
Solve a radical equation by isolating the root and squaring both sides. Squaring can introduce extraneous solutions that do not satisfy the original equation, so you must check every answer.
Worked example
Solve √(x + 5) = x − 1. Square both sides: x + 5 = x^2 − 2x + 1, so x^2 − 3x − 4 = 0, giving (x − 4)(x + 1) = 0 and x = 4 or x = −1. Check: x = 4 gives √9 = 3 ✓; x = −1 gives √4 = 2 but x − 1 = −2 ✗, so x = 4 only.
Practice questions
- Solve √(2x + 1) = 3.
- Solve √(x + 6) = x and check for extraneous solutions.
- Solve 1/(x − 2) = 3 for x.
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 Radicales y Racionales
Resuelve una ecuación radical aislando la raíz y elevando ambos lados al cuadrado. Elevar al cuadrado puede introducir soluciones extrañas que no satisfacen la ecuación original, por lo que debes verificar cada respuesta.
Ejemplo: Resuelve √(x + 5) = x − 1. Eleva al cuadrado ambos lados: x + 5 = x^2 − 2x + 1, así que x^2 − 3x − 4 = 0, dando (x − 4)(x + 1) = 0 y x = 4 o x = −1. Verifica: x = 4 da √9 = 3 ✓; x = −1 da √4 = 2 pero x − 1 = −2 ✗, así que solo x = 4.
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