Square Roots & Cube Roots
Aligned to 8.EE.A.2 — Common Core State Standards for Mathematics.
What this lesson teaches
√p answers "what number squared equals p?" and ∛p answers "what number cubed equals p?" Solving x^2 = p gives x = ±√p (two solutions); solving x^3 = p gives x = ∛p (one solution).
Worked examples
Example 1
Solve x^2 = 49. Take the square root of both sides: x = ±√49 = ±7, so x = 7 or x = −7. For x^3 = 27, x = ∛27 = 3, since 3 × 3 × 3 = 27.
Example 2
Solve x² = 144: x = ±12. Both 12 and −12 square to 144, so both are solutions.
Example 3
Cube roots keep the sign: ∛(−8) = −2, since (−2)³ = −8. A negative number has no real square root but always has a real cube root.
Practice questions
- Evaluate √81.
- Solve x^2 = 144.
- Solve x^3 = 125 and explain why it has only one real 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
Raíces Cuadradas y Cúbicas
√p responde "¿qué número al cuadrado da p?" y ∛p responde "¿qué número al cubo da p?" Resolver x^2 = p da x = ±√p (dos soluciones); resolver x^3 = p da x = ∛p (una solución).
Ejemplo 1: Resuelve x^2 = 49. Saca la raíz cuadrada de ambos lados: x = ±√49 = ±7, así que x = 7 o x = −7. Para x^3 = 27, x = ∛27 = 3, porque 3 × 3 × 3 = 27.
Ejemplo 2: Resuelve x² = 144: x = ±12. Tanto 12 como −12 elevados al cuadrado dan 144, así que ambas son soluciones.
Ejemplo 3: Las raíces cúbicas conservan el signo: ∛(−8) = −2, porque (−2)³ = −8. Un número negativo no tiene raíz cuadrada real pero siempre tiene raíz cúbica real.
More Expressions & Equations lessons
Teach this lesson today
An AI tutor that guides with questions instead of just giving answers — all K–12 core subjects, every child in the family.
Start free — no card required