8.EE.A.2 8th Grade Expressions & Equations

Square & Cube Roots

Use square root and cube root symbols to represent solutions to equations, and evaluate the roots of small perfect squares and cubes.

How to explain it

At this standard, students evaluate square roots of perfect squares and cube roots of perfect cubes, use radical symbols to write solutions to x² = p and x³ = p, and recognize that the root of a non-perfect power is irrational.

The anchor students hold onto: Perfect squares give whole-number square roots and perfect cubes give whole-number cube roots. The root of a non-perfect number like √2 is irrational.

Students will use these roots to interpret 8.NS.A.2 irrational approximations on a number line, and to classify the length outputs of 8.G.B.7-8 Pythagorean theorem problems.

Worked examples

Example 1 Perfect Square

Solve x² = 49.

Step 1Take the square root of both sides.

Step 2x = √49.

Step 37² = 49, so x = 7.

Answerx = 7

Example 2 Perfect Cube

Solve x³ = 64.

Step 1Take the cube root of both sides.

Step 2x = ∛64.

Step 34³ = 64, so x = 4.

Answerx = 4

Example 3 Irrational Root

Solve x² = 2.

Step 1Take the square root of both sides.

Step 2x = √2.

Step 3√2 ≈ 1.414.. — irrational (never ends or repeats).

Answerx = √2 (irrational)

Common mistakes

What students write Reading √49 as 24.5 by taking half of 49.

The fix A square root is not half. √49 = 7 because 7² = 49.

What students write Splitting a root over addition: √(4+9) = √4 + √9.

The fix Roots do not distribute. Add under the radical first: √(4+9) = √13 ≈ 3.61.

Teacher tip

Head off the two predictable errors before they happen. First: A square root is not half. √49 = 7 because 7² = 49. Second: Roots do not distribute. Add under the radical first: √(4+9) = √13 ≈ 3.61.