Cube Root (∛)

Definition

The cube root, denoted by the symbol ∛, is a mathematical operation that finds the value that, when multiplied by itself three times, equals the original number. It is one of the fundamental operations in algebra and is closely related to the concepts of exponents and radicals.

5 Must Know Facts For Your Next Test

1. The cube root operation is used to simplify expressions with roots, as described in Section 8.1 Simplify Expressions with Roots.
2. Cube roots are used to simplify radical expressions, as discussed in Section 8.2 Simplify Radical Expressions.
3. Dividing radical expressions, as covered in Section 8.5 Divide Radical Expressions, often involves the use of cube roots.
4. Solving radical equations, as explored in Section 8.6 Solve Radical Equations, may require the use of cube root properties.
5. Cube roots are used in functions that involve radicals, as discussed in Section 8.7 Use Radicals in Functions.

Review Questions

• Explain how the cube root operation is used to simplify expressions with roots.
  • The cube root operation is used to simplify expressions with roots by finding the value that, when multiplied by itself three times, equals the original number. For example, to simplify $\sqrt[3]{27}$, we can use the cube root to find that $\sqrt[3]{27} = 3$, since $3 \times 3 \times 3 = 27$. This allows us to rewrite the expression without the cube root symbol.
• Describe how cube roots are used to simplify radical expressions.
  • Cube roots are used to simplify radical expressions by rewriting them in a more simplified form. For instance, $\sqrt[3]{8}$ can be rewritten as $2$ because $2^3 = 8$. This simplification process is crucial when working with more complex radical expressions that involve cube roots, as it helps to reduce the expression to a more manageable form.
• Analyze the role of cube roots in solving radical equations.
  • Solving radical equations often requires the use of cube root properties. When a radical equation contains a cube root, the equation can be simplified by raising both sides to the power of 3 to isolate the variable. This process eliminates the cube root symbol and allows for the equation to be solved using standard algebraic methods. The ability to effectively use cube roots is essential for successfully solving a variety of radical equations.

Related terms

Radical: A radical is a symbol (√) that indicates the root of a number, such as a square root (√) or a cube root (∛).

Exponent: An exponent is a number that represents the power to which a base number is raised. For example, in the expression $x^3$, the exponent is 3, indicating that $x$ is multiplied by itself three times.

Perfect Cube: A perfect cube is a number that can be expressed as the cube of an integer. For example, 8 is a perfect cube because it can be written as $2^3$.