Simplifying Radical Expressions II

A radical expression is not in simplest or standard form if there is a radical in the denominator. To simplify the expression we ratioalize the denominator.

A. Monomial Denominator

1. To simplify factor radicand as a product of prime factors.

2. Multiply numerator and denominator by radical whose order is the same as the order of radical in the denominator. The radicand is chosen so that the product of the original radicand and radicand of multiplier will give exponents which are divisible by index. Factors in radicand of multiplier should all have exponents less than index of radical.

3. Use property II to multiply radicals together.

II. Product Property

4. Use property I to simplify radical(s).

I. If n is even

if n is odd

Examples:

 

B. Binomial Denominator

To simplify a radical expression with one or two second order radicals in a binomial denominator, multiply numerator and denominator by the conjugate of the denominator. Remember the conjugate of a + b is a - b and the conjugate of a - b is a + b.

Exam