CCSS.Math.Content.8.EE.A.2
The Standard
Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
Common Core State Standards for Mathematics · Expressions and Equations
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students solve square and cube equations using radical symbols. They evaluate roots of familiar perfect squares and cubes. They also recognize that √2 cannot be written as a ratio of integers.
What Mastery Looks Like
- Students correctly evaluate familiar perfect square and perfect cube roots. They distinguish the principal square root from both solutions of a square equation and identify √2 as irrational.
Common Misconceptions
- Students often write √49 as ±7, instead of using 7 for the radical and ±7 for the equation’s solutions. They may give two answers for a cube equation or treat √2’s decimal approximation as an exact fraction.
How to Assess It
- Give this exit ticket: Evaluate √81, solve x² = 81, evaluate ∛64, and explain why √2 is irrational.
Lesson moves
Ways to Teach It
Build square arrays and cube models with tiles or blocks, then connect each model’s total pieces to its side length and root.
Ask students to explain why √49 equals 7, while x² = 49 has two solutions.
Play a matching game with cards showing powers, root expressions, equations, and solutions, including positive and negative values.
Find the side length of a square garden from its area and the edge length of a cube-shaped box from its volume.
Free download
Printable 8.EE.A.2 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.8.EE.A.2, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetLearning progression
Where This Standard Sits
See the whole path on the Expressions & Equations progression map.
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.8.NS.A.1
Understanding rational versus irrational numbers supports recognizing why a root such as √2 is not a rational number.
- CCSS.Math.Content.6.EE.A.1
Students must understand squares and cubes as exponents before interpreting square and cube roots as their inverse operations.
- CCSS.Math.Content.6.EE.B.5
Substituting values to check equations supports seeing square and cube roots as the numbers that make x²=p or x³=p true.
What This Unlocks
Mastery here sets students up for these next.
- CCSS.Math.Content.8.G.B.7
Finding an unknown side with the Pythagorean Theorem requires solving x² = p and interpreting square roots.
- CCSS.Math.Content.HSA-REI.B.4
Solving quadratics often requires using square roots and recognizing irrational roots, extending the simpler x² = p cases.
- CCSS.Math.Content.HSA-REI.B.4a
Solving the completed-square form and deriving the formula require taking square roots of squared expressions and interpreting both solutions.
- CCSS.Math.Content.HSN-RN.A.1
Square and cube root notation and meanings prepare students to see fractional exponents as another way to write roots.
- CCSS.Math.Content.8.G.B.8
Finding coordinate distance requires turning d² into d with square roots, including exact roots and irrational lengths.
- CCSS.Math.Content.HSF-TF.C.8
Solving sin² or cos² from the identity requires square-root notation and choosing a sign using the quadrant.
Keep exploring
Related Standards
- CCSS.Math.Content.7.EE.B.4a
Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these form...
- CCSS.Math.Content.6.EE.B.7
Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative r...
- CCSS.Math.Content.8.NS.A.2
Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate th...
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