Maryland Math 8.NOS.B.4.b

Math8th GradeNumber and Operation Sense

The Standard

8.NOS.B.4: Use square and cube roots to represent solutions to equations and describe numbers.

Evaluate square roots of perfect squares from 1 to 100 and cube roots of perfect cubes from 1 to 125 by inspection.

Maryland College and Career Ready Standards for Mathematics (2025) · REASON WITH EXPONENTS TO EXPRESS AND INTERPRET QUANTITIES.

Teacher's field guide

What Students Need to Do: Students recognize square roots of perfect squares up to 100 and cube roots of perfect cubes up to 125. They use multiplication facts to name each root without a calculator.
What Mastery Looks Like: A student sees √81 and says 9 because 9 × 9 = 81. They see ∛64 and say 4 because 4 × 4 × 4 = 64.
Common Misconceptions: Students may give both 8 and −8 for √64, rather than the single value 8. Some confuse square and cube roots, or say ∛27 is 9 because 3 × 9 = 27.
How to Assess It: Exit ticket: Find √49, √81, and ∛125 without a calculator. Write a multiplication fact that checks each answer.

Lesson moves

Give pairs 36 square tiles and 27 unit cubes; have them build a square and a cube, then name each side length.
Ask partners: Why is √64 equal to 8, while ∛64 equals 4? Have them write a multiplication fact for each.
Use cards marked √36, √100, ∛27, and ∛125; students race to match them with 6, 10, 3, and 5.
Describe a square patio covered with 81 equal tiles and ask how many tiles line each edge.

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