Math with Mr. J: Introduction to Cube Roots

Key Concepts

Cubing a Number

• Cubing: Raising a number to the power of three.
• Expression: For a number 'a', cubing is written as 'a³'.
• Example: 2³ = 2 x 2 x 2 = 8.

Cube Roots

• Definition: The opposite (inverse) of cubing a number.
• Problem: Finding what number, when multiplied by itself three times, equals a given value.
• Symbol: Typically represented by the radical sign with a small three (∛).

Examples and Explanation

Example 1: Cube Root of 8

• 2³ = 8, thus ∛8 = 2.
• Relationship: 2³ = 8 and ∛8 = 2.

Example 2: Cube Root of 125

• 5³ = 125, thus ∛125 = 5.
• Relationship: 5³ = 125 and ∛125 = 5.

Example 3: Cube Root of 64

• 4³ = 64, thus ∛64 = 4.
• Step-by-Step:
  • 4 x 4 = 16
  • 16 x 4 = 64

Example 4: Cube Root of 27

• 3³ = 27, thus ∛27 = 3.
• Step-by-Step:
  • 3 x 3 = 9
  • 9 x 3 = 27

Summary

• To find a cube root, determine what number, when multiplied three times by itself, equals the number under the cube root symbol.
• Practice examples:
  • ∛8 = 2
  • ∛125 = 5
  • ∛64 = 4
  • ∛27 = 3

Note: Always remember the relationship between cubing a number and finding the cube root: cube and cube root are inverse operations.