Introduction to Cube Roots

Overview

• A cube root finds the number that, when multiplied by itself three times, equals the original number under the cube root symbol.
• Cube roots are the inverse operation of cubing a number.

Cubing a Number

• Definition: Raising a number to the power of 3.
• Example:
  • (2^3 = 2 \times 2 \times 2 = 8)

Understanding Cube Roots

• Concept: Reverse of cubing a number.
• Process: Determine which number multiplied by itself three times produces the original number.

Examples

Example 1

• Cubing:
  • (2^3 = 8)
• Cube Root:
  • (\sqrt[3]{8} = 2)
• Relationship:
  • (2^3 = 8) and (\sqrt[3]{8} = 2)

Example 2

• Cubing:
  • (5^3 = 5 \times 5 \times 5 = 125)
• Cube Root:
  • (\sqrt[3]{125} = 5)
• Relationship:
  • (5^3 = 125) and (\sqrt[3]{125} = 5)

Example 3

• Cube Root:
  • Find (\sqrt[3]{64})
  • Calculation: (4^3 = 4 \times 4 \times 4 = 64)
  • Result: (\sqrt[3]{64} = 4)

Example 4

• Cube Root:
  • Find (\sqrt[3]{27})
  • Calculation: (3^3 = 3 \times 3 \times 3 = 27)
  • Result: (\sqrt[3]{27} = 3)

Conclusion

• To find a cube root, identify the number that multiplies by itself three times to equal the number under the cube root symbol.
• Cube roots and cubing are directly related as inverse operations.