Rationalizing Denominators Calculator Online

Rationalizing the denominator is required when a mathematical expression has a radical (or root) in the denominator. The purpose of rationalization is to eliminate these radicals to simplify the expression, making it easier to work with, especially in further calculations or applications. The Rationalizing Denominators Calculator automates this process: input an expression, and it provides a simplified version with a rationalized denominator.

Formulae for Rationalization

To rationalize denominators, different scenarios and corresponding methods are used. Here are the general cases:

• Radical over Radical: (a * n√b) / (x * k√y)
• Sum over Radical: (a * n√b + c * m√d) / (x * k√y)
• Radical over Sum: (a * √b) / (x * √y + z * √u)
• Sum over Sum: (a * √b + c * √d) / (x * √y + z * √u)

Each formula requires multiplying both numerator and denominator by a conjugate or a similar radical form to eliminate radicals from the denominator.

Useful Conversions and Terms Table

For those new to the topic or needing a quick reference, below is a table of common terms and conversions used in the process of rationalizing denominators:

Term	Definition	Example
Radical	An expression that includes a root, such as a square root or cube root	sqrt(9) = 3
Conjugate	The opposite sign between two terms in a binomial, used to eliminate radicals	sqrt(a) + sqrt(b) to sqrt(a) – sqrt(b)
Denominator	The bottom part of a fraction	In a/b, b is the denominator

Step-by-Step Example

Consider rationalizing the expression (3√5) / (2√2):

1. Multiply both the numerator and the denominator by √2:scss

1. (3√5) / (2√2) * (√2 / √2) = (3√10) / 4
2. The denominator is now rationalized, as it contains no radicals.

This example illustrates how using the calculator simplifies the process, providing quick and accurate results.

Most Common FAQs