Home›Lesson Plans›Mathematics›Expressions & Equations · Grade 8

Square & Cube Roots

Eighth graders learn square roots and cube roots — the operations that undo squaring and cubing — and recognize perfect squares and perfect cubes whose roots are whole numbers.

Grade 8Roots50 minutes1 class periodGradual ReleaseExplicit teaching4 StandardsCommon Core
Start the Lesson
Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Find square roots.
  • ✓Find cube roots.
  • ✓Recognize perfect squares/cubes.
  • ✓Know roots undo powers.
Essential Question

If 5² = 25, then what number squared gives 25? That’s the square root! How do roots undo powers, and which numbers have whole-number roots?

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Lesson Phases
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Vocabulary Terms
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Standards Aligned
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Interactive Task
Model · Interactive Tool

The Root Explorer

Project this and change n. See how squaring and its square root undo each other — and the same for cubing and cube roots!

√ Explore square & cube rootsTry it
Number n = 5

The Lesson · Gradual Release (I Do · We Do · You Do)

50 minutes, five moves

Tap any phase to open the teacher moves and student actions.

1

Launch — Undoing a Power

5 min

5² = 25 — so what number squared gives 25?

👩‍🏫 Teacher Moves

  • Show 5² = 25.
  • Ask for the reverse.
  • Set the goal: roots.

🎒 Student Actions

  • See the square.
  • Reverse it.
  • Predict the root.
2

I Do — Roots Undo Powers

10 min

Teacher models.

👩‍🏫 Teacher Moves

  • Square root undoes squaring.
  • Cube root undoes cubing.
  • Find perfect squares/cubes.

🎒 Student Actions

  • Learn square root.
  • Learn cube root.
  • Find perfects.
3

We Do — Explore Together

13 min

Class uses the Root Explorer.

👩‍🏫 Teacher Moves

  • Change n.
  • See the power and its root.
  • Note perfect squares/cubes.

🎒 Student Actions

  • Set n.
  • See the root.
  • Note perfects.
4

You Do — On Your Own

12 min

Students find roots.

👩‍🏫 Teacher Moves

  • Find square roots.
  • Find cube roots.
  • Identify perfect squares/cubes.

🎒 Student Actions

  • Find roots.
  • Find cube roots.
  • Identify perfects.
5

Close — Close

5 min

One root.

👩‍🏫 Teacher Moves

  • Give a perfect square or cube.
  • Find its root.
  • Hand out the exit ticket.

🎒 Student Actions

  • Find the root.
  • Explain it.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics.

CCSS
8.EE.2

Use square root and cube root symbols to represent solutions.

CCSS
8.EE.2

Evaluate square roots of perfect squares and cube roots of perfect cubes.

CCSS
8.NS.2

Approximate the value of irrational roots.

SMP
MP.7

Use the structure connecting powers and roots.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Perfect-square/cube reference.
  • Sentence frame: “√___ = ___ because ___.”
  • Use a squares chart.

Support & Access

IEP / 504
  • Start with small perfect squares.
  • Use a squares/cubes chart.
  • Connect to the power.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Approximate non-perfect roots.
  • Solve x² = 49.
  • Simplify roots.
Materials

What to gather

  • 📽️Projector / board
  • 🧮Calculators
  • 💻The Root Explorer
  • 📄Squares/cubes charts
  • ✏️Pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

square roota number that, squared, gives anothercube roota number that, cubed, gives anotherperfect squarea whole number squared (4, 9, 16…)perfect cubea whole number cubed (8, 27, 64…)radicalthe root symbol √radicandthe number under the rootinversethe opposite operationexponenta power
Evaluate

Exit Ticket

Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.

QUESTION 1
What is √64?
8 (because 8² = 64).
QUESTION 2
What is ∛27 (the cube root of 27)?
3 (because 3³ = 27).
QUESTION 3
What operation does a square root undo?
Squaring (raising to the 2nd power).

Going deeper? Non-perfect roots.

Have students approximate √50 by finding the two perfect squares it falls between (49 and 64). A printable roots sheet is in the Math library.

Study · Flashcards

Study the key terms

Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.

🃏 Square & Cube RootsFlip
Card 1
Term
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Meaning
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Practice · Quiz

Check your understanding

A quick self-check with instant feedback, drawn from this lesson’s key terms.

📝 Square & Cube RootsQuiz
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Question 1
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Practice · Worksheet

Printable worksheet

A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.

🖨️ Square & Cube RootsPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: cube root, exponent, inverse, perfect cube, perfect square, radical, radicand, square root
  1. a whole number cubed (8, 27, 64…)
  2. the opposite operation
  3. a whole number squared (4, 9, 16…)
  4. the number under the root
  5. a number that, squared, gives another
  6. a power
  7. the root symbol √
  8. a number that, cubed, gives another

Part B · Show what you learned

  1. What is √64?
  2. What is ∛27 (the cube root of 27)?
  3. What operation does a square root undo?
Answer key — Part A: 1) perfect cube · 2) inverse · 3) perfect square · 4) radicand · 5) square root · 6) exponent · 7) radical · 8) cube root
Part B: 1) 8 (because 8² = 64). 2) 3 (because 3³ = 27). 3) Squaring (raising to the 2nd power).