Edge Lengths and Volumes

Student Summary

For a square, its side length is the square root of its area. For example, this square has an area of 16 square units and a side length of 4 units.

Both of these equations are true:

42=16\displaystyle 4^2=16

16=4\displaystyle \sqrt{16}=4

A square with a side length of 4 units on a square grid.

For a cube, the edge length is the cube root of its volume. For example, this cube has a volume of 64 cubic units and an edge length of 4 units:

Both of these equations are true:

43=64\displaystyle 4^3=64

643=4\displaystyle \sqrt[3]{64}=4

A solid cube composed of 64 unit cubes. Each edge length is 4 unit cubes.

643\sqrt[3]{64} is pronounced “the cube root of 64.” Here are some other values of cube roots:

83=2\sqrt[3]{8}=2 because 23=82^3=8

273=3\sqrt[3]{27}=3 because 33=273^3=27

1253=5\sqrt[3]{125}=5 because 53=1255^3=125

Visual / Anchor Chart

Standards

Addressing
8.EE.2

8.EE.A.2

8.EE.2

8.EE.A.2

8.EE.2

8.EE.A.2

8.NS.2

8.NS.A.2