Rationalizing the Denominator Steps
This section covers the important technique of rationalizing denominators, which is crucial for simplifying radical expressions. The rationalizing the denominator steps are explained for both one-term and two-term denominators.
For one-term denominators:
- Multiply both numerator and denominator by the radical in the denominator.
- Simplify the resulting expression.
Example: 1 / √3 = 1×√3 / √3×√3 = √3 / 3
For two-term denominators involving a sum or difference of radicals:
- Multiply both numerator and denominator by the conjugate of the denominator.
- Expand and simplify the resulting expression.
Example: 1 / √2+√3 = √2−√3 / (√2+√3√2−√3) = √2−√3 / 2−3 = √2 - √3
The page provides several detailed examples of this process, including cases with variables and more complex expressions.
Highlight: Rationalizing the denominator is an essential skill for simplifying radical expressions and is often required in more advanced mathematical operations.
The examples on this page demonstrate how to apply these techniques to increasingly complex problems, providing students with a solid foundation for working with radical expressions.
