# Lesson 13

Cube Roots

### Lesson Narrative

In this lesson, students continue to work with cube roots, moving away from the geometric interpretation in favor of the algebraic definition. They approximate cube roots and locate them on the number line. They see their first negative cube root, and locate it on the number line.

### Learning Goals

Teacher Facing

• Determine the whole numbers that a cube root lies between, and explain (orally) the reasoning.
• Generalize a process for approximating the value of a cube root, and justify (orally and in writing) that if $x^3=a$, then $x=\sqrt{a}$.

### Student Facing

Let’s compare cube roots.

### Student Facing

• When I have a cube root, I can reason about which two whole numbers it is between.

### CCSS Standards

The cube root of a number $$n$$ is the number whose cube is $$n$$. It is also the edge length of a cube with a volume of $$n$$. We write the cube root of $$n$$ as $$\sqrt{n}$$.
For example, the cube root of 64, written as $$\sqrt{64}$$, is 4 because $$4^3$$ is 64. $$\sqrt{64}$$ is also the edge length of a cube that has a volume of 64.