Maryland Math 8.NOS.B.4.a
The Standard
- 8.NOS.B.4
- Use square and cube roots to represent solutions to equations and describe numbers.
Use square and cube roots symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number.
Maryland College and Career Ready Standards for Mathematics (2025) · REASON WITH EXPONENTS TO EXPRESS AND INTERPRET QUANTITIES.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use square roots to name both numbers whose squares equal a given positive number. They use cube roots to name the one number whose cube equals it, including when the number is a fraction.
What Mastery Looks Like
- A student writes ±√(25/36) = ±5/6, but ∛(8/27) = 2/3. They check each answer by raising it to the given power.
Common Misconceptions
- Students often give only the positive solution for a square. Some think √p means both positive and negative values, or give two solutions for a cube.
How to Assess It
- Exit ticket: Solve x² = 9/16 and x³ = 27/64 using root symbols. Check each solution by substitution.
Lesson moves
Ways to Teach It
Give pairs a 4-by-4 unit grid; shade a 3-by-3 square, then write both numbers whose squares equal its area.
Ask: Why does x² = 1/4 have two solutions, while x³ = 1/8 has one? Have students explain using signs.
Play root-match: match x² = 25/36 and x³ = 8/27 cards to solution cards, then check by substitution.
Present a square garden with area 3/4 square meter; students write its side length as √(3/4) meters and explain why length cannot be negative.
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Related Standards
- 7.AT.C.8.a
Write equations of the form px + q = r and p(x + q) = r where p, q, and r are specific rational numbers.
- 7.NOS.A.2.b
Interpret quotients of rational numbers in context and represent division of signed numbers in different forms, such as −(p/q) = (−p)/q = p/(−q) when the diviso...
- 6.AT.C.8.b
Write and solve one-step equations of the form x + p = q, x − p = q, px = q and x/p = q for cases in which p, q and x are all nonnegative rational numbers.
- 8.NOS.B.4
Use square and cube roots to represent solutions to equations and describe numbers.
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