Objective: Rationalize denominators for radical expressions containing one or two terms in the denominator.
A radical expression is not considered "simplified" unless it does not contain any radicals in the denominator. Therefore, when a radical expression does contain radicals in the denominator, rationalizing the denominator is the process by which you write an equivalent expression that does not contain radicals in the denominator. The process is slightly different when the denominator contains one term than when the denominator contains two terms, but both rely on the concept of multiplying the fraction by a value of 1. When containing one term in the denominator, simply multiply the numerator and the denominator by the radical expression in the denominator of the radical expression. When containing two terms in the denominator, you must multiply the expression by the conjugate of the denominator. Conjugates are formed by changing the sign between two terms (eg. 3 + 4x and 3 - 4x are considered conjugates).
Watch the video below to learn how to rationalize denominators.
Complete the worksheet attachment below and then check your answers using the solutions attachment. Once you have completed these exercises, click the link to advance to the next lesson.