Name: Roots and Equations Worksheet with Quadratic and Cubic Equations 8.EE.A.2
SKU: 636cee3dcff5152f353a913e
Price: 39.99 USD
Availability: InStock

About this resource

What's inside this resource

A printable pdf worksheet for 8th grade math about roots and equations. Students will practice to:

Solve quadratic equations with perfect squares

Solve quadratic equations that have rational answers

Solve quadratic equations that have irrational answers

Remember that there are often two solutions to quadratic equations

Solve cubic equations with perfect cubes

Solve cubic equations that have rational answers

Solve cubic equations that have irrational answers

All answers are included.

In the classroom

Teaching tips & learning objectives

Learning objectives

Solve equations of the form x squared = p, giving both the positive and negative real solutions.
Solve equations of the form x cubed = p, including cases with negative or fractional p.
Simplify square and cube roots of large numbers and fractions to exact form.
Classify a given square root as rational or irrational.

Teaching tips

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 full worked-solution answer key, which shows every simplification step rather than only the final answer.

Skills covered

Solving quadratic equations x squared = p -- students find both real solutions (e.g., x = ±7) across 40 perfect-square and non-perfect-square items.
Solving cubic equations x cubed = p -- students find the single real solution, including for negative values of p, across 40 items.
Simplifying radicals -- students reduce square and cube roots of large numbers and fractions to exact simplified form.
Rational vs. irrational classification -- students sort given square roots into a rational/irrational table in the Classify section.

Good to know

Questions teachers ask about this resource

Why do some problems have two solutions while others have only one?

Equations of the form x squared = p have two real solutions, positive and negative, while x cubed = p equations have only one real solution, since a negative number cubed stays negative -- the worksheet's own instruction to give all solutions applies differently to each equation type.

What does the Classify section ask students to do differently from the rest of the worksheet?

Instead of solving an equation, students sort a list of square roots -- including ones with fractional radicands -- into a table by whether each is rational or irrational.