Square and cube roots worksheet

Grade 8 math, Common Core 8.EE.A.2. 10 problems with an answer key and worked steps. Free to print, and you can make new problems any time.

By the StudyWiz teamUpdated October 23, 2026How we write our pages

NameDate

Square and cube roots

Grade 8 math, Common Core 8.EE.A.2

Evaluate each root or solve each equation.

  1. 1.
    √81
  2. 2.
    A cube has a volume of 125 cm³. How long is each edge?
  3. 3.
    √2564
  4. 4.
    Solve: x² = 169
  5. 5.
    √81100
  6. 6.
    √196
  7. 7.
    A cube has a volume of 216 cm³. How long is each edge?
  8. 8.
    √6425
  9. 9.
    ∛125
  10. 10.
    A cube has a volume of 27 cm³. How long is each edge?
Free worksheets for grades 6 to 8 from StudyWiz, with answer keys: studywiz.online/worksheets

Answer key: Square and cube roots

Grade 8 math. Each answer has a few worked steps, to help check the method as well as the answer.

  1. 1. 9

    9² = 81

  2. 2. 5 cm

    ∛125 = 5

  3. 3. 58

    √25 = 5 and √64 = 8

  4. 4. x = 13 or x = −13

    13² = 169 and (−13)² = 169

  5. 5. 910

    √81 = 9 and √100 = 10

  6. 6. 14

    14² = 196

  7. 7. 6 cm

    ∛216 = 6

  8. 8. 85

    √64 = 8 and √25 = 5

  9. 9. 5

    (5)³ = 125

  10. 10. 3 cm

    ∛27 = 3

The answer key prints on its own page. You’re welcome to print and copy these worksheets for your own kids or class.

About square and cube roots

A square root undoes squaring: √81 = 9 because 9² = 81. A cube root undoes cubing: ∛64 = 4 because 4³ = 64. The equation x² = 49 has two solutions, 7 and −7, because both square to 49, but x³ = 125 has only one, 5.

Worked example 1

√49
  1. Step 1.√4 = 2 and √9 = 3

Answer: 23

Worked example 2

√144
  1. Step 1.12² = 144

Answer: 12

Worked example 3

A square garden has an area of 25 m². How long is each side?
  1. Step 1.√25 = 5

Answer: 5 m

Watch out for

  • x² = 49 has two answers: x = 7 or x = −7.
  • The cube root of a negative number is negative: ∛(−27) = −3.
  • Learn the squares to 15² and the cubes to 6³: they come up all the time.

Practice square and cube roots online

On StudyWiz, your kid can practice square and cube roots with 5-question quizzes that are checked as they go, with an explanation for every answer. When a homework problem is the trouble, Wiz gives a hint for each step instead of the answer.

More grade 8 math worksheets

More from Expressions and equations:

Other grade 8 topics:

See all 8th grade math worksheets, or switch to grade 6 or grade 7.

Keep reading

Try Wiz with tonight’s homework

Free to start, no card needed. Each kid gets 3 homework questions, 5 practice quizzes and 1 writing review a day on the free plan.