Rationalize Denominator Calculator

Rationalizing the denominator means rewriting a fraction so that the denominator contains only rational numbers (i.e., no radicals).

Case 1: Monomial Denominator (e.g., 1/√2)

• Multiply both the numerator and the denominator by the radical in the denominator.
• Example: For 3 / √5, multiply top and bottom by √5 to get (3√5) / 5.

Case 2: Binomial Denominator (e.g., 1 / (2 + √3))

• Find the conjugate of the denominator. The conjugate is found by changing the sign between the two terms (e.g., the conjugate of 2 + √3 is 2 - √3).
• Multiply both the numerator and the denominator by this conjugate.
• This uses the difference of squares formula: (a+b)(a-b) = a² - b², which eliminates the radical.