Lesson 14: Edge Lengths and Volumes

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:

$\displaystyle 4^2=16$

$\displaystyle \sqrt{16}=4$

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:

$\displaystyle 4^3=64$

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

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

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

$\sqrt[3]{8}=2$ because $2^3=8$

$\sqrt[3]{27}=3$ because $3^3=27$

$\sqrt[3]{125}=5$ because $5^3=125$

Visual / Anchor Chart

Standards

Addressing

8.EE.2

Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Know square roots of perfect squares up to 225 and cube roots of perfect cubes up to 125. Know that the square root of a non-perfect square is irrational.

8.NS.2

Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions.