Roots and Equations Worksheet with Quadratic and Cubic Equations 8.EE.A.2

Solve square equations, giving both real solutions when the right-hand side is positive.

Solve cube equations with positive, negative or fractional values.

Express square and cube roots in exact form.

Assign the Perfect Squares/Cubes sections before the Square Roots/Cube Roots sections, since the worksheet's own sequence moves from whole-number perfect powers to irrational exact-form answers.

Use the Classify section as a quick formative check after the roots sections, since it tests the rational-versus-irrational distinction those sections build toward.

Check work against the answer section, which includes worked steps and exact answers.

Solving quadratic equations x squared = p -- students find both real solutions for positive right-hand sides (e.g., x = ±7) and recognize that x² = 0 has one real solution.

Solving cubic equations x cubed = p -- students find the single real solution, including for negative values of p, across the cube-equation sections.

Simplifying radicals -- students reduce square and cube roots of large numbers and fractions to exact simplified form.