8.EE.2: Square Roots and Cube Roots
Also written as 8.EE.A.2 and CCSS.MATH.CONTENT.8.EE.A.2 · Cluster: Work with radicals and integer exponents.
The Official Wording
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. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
Common Core State Standards, Grade 8, Expressions & Equations · Read it at the source · Checked October 14, 2026
What 8.EE.2 Means in Plain English
Eighth graders solve x² = 49 with a square root, x = 7 or x = -7, and x³ = 64 with a cube root, x = ∛64 = 4. They know small perfect squares and cubes by sight and leave x = √2 exact when no whole number works.
Students also learn that √2 is irrational: no fraction squares to exactly 2, which ties this standard to 8.NS.1. Roots come back in the Pythagorean theorem (8.G.7), and in high school x² = p becomes one way to solve a quadratic (HSA-REI.4).
8.EE.2 I Can Statements
- I can solve x² = p and x³ = p with root symbols.
- I can find square roots and cube roots of small perfect squares and cubes.
- I can tell when a root is whole and when it is irrational.
8.EE.2 Worked Example
A patio and a planter whose sides come out whole, then a second patio whose side has to stay a square root.
A square patio covers 144 square feet and a cube-shaped planter holds 27 cubic feet of soil. How long is a side of each? A second square patio covers 50 square feet: how long is its side?
- Write an equation for the first patio: a side times itself is the area.s² = 144
- Undo the square with a square root. The equation also has the solution -12, but a side length cannot be negative.s = √144 = 12 feet
- The planter is a cube, so its edge used as a factor three times gives the volume. Undo that with a cube root.e³ = 27, so e = ∛27 = 3 feet
- 50 is not a perfect square, so the exact side stays a root. Bracket it to get a feel for its size.s² = 50, so s = √50 feet, between 7 and 8 because 7² = 49 and 8² = 64
Check it: Multiply back: 12 × 12 = 144 and 3 × 3 × 3 = 27. For √50, 7.1² = 50.41, just over 50, so the side is just under 7.1 feet.
Common Mistakes with 8.EE.2
Dividing by 2 instead of taking the root
√36 = 18
Try this: Multiply back before writing a root: 18 × 18 = 324, not 36. The root of 36 is 6, since 6 × 6 = 36.
Missing the negative solution
x² = 49, so x = 7
Try this: Substitute -7 too: (-7)² = 49, so x² = 49 has two solutions, 7 and -7, unless x is a length.
Calling a rounded root exact
√2 = 1.41
Try this: Square the decimal to test it: 1.41² = 1.9881, not 2. Keep √2 as the exact answer and 1.41 as an estimate.
Where 8.EE.2 Fits
Practice 8.EE.2
Quick Check
- Solve x² = 121.
- Solve x³ = 1/8.
- Is √64 rational or irrational? What about √65?