Montana Math MT.8.EE.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 and evaluate square roots of small perfect squares and cube roots of small perfect cubes.
2026 Montana Mathematics Content Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use square root and cube root symbols to solve equations with positive rational numbers. They evaluate roots of small perfect squares and cubes, then check by squaring or cubing.
What Mastery Looks Like
- For x² = 9/16, a student writes x = ±√(9/16) = ±3/4. For x³ = 8/27, they write x = ∛(8/27) = 2/3.
Common Misconceptions
- Students may give only 5 as a solution to x² = 25, or say √25 equals both 5 and −5. Some divide by 2 or 3 instead of taking a root.
How to Assess It
- On an exit ticket, ask: Solve x² = 4/9 and x³ = 1/8 using radical symbols, then give every numerical solution.
Lesson moves
Ways to Teach It
Give pairs 16 square tiles and 8 linking cubes to build a square and a cube, then label each side length.
Ask students to explain in writing why x² = 36 has two solutions but x³ = 27 has one.
Have students match cards showing x² = 25 and x³ = 64 with cards showing their radical and numerical solutions.
Show a square garden with an area of 81 square feet and a cube box with a volume of 64 cubic feet; find their side lengths.
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Printable MT.8.EE.2 Worksheet
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Related Standards
- MT.7.EE.1
Use properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients and generate equivalent expressions.
- MT.7.EE.4
Use variables to represent quantities and construct simple equations and inequalities to solve problems in context. This standard should incorporate cultural co...
- MT.7.EE.3
Write and solve one- and two-step equations including problems in context with rational numbers, convert between forms as appropriate, and assess the reasonable...
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