Dividing Radical Expressions

Quotient Property of Radicals 0, For real numbers a and b, b where n>1, ex:

In general, a radical expression is simplified when: The radicand contains no fractions. No radicals appear in the denominator. (Rationalization) The radicand contains no factors that are nth powers of an integer or polynomial.

Simplify each expression. When there is a factor in common, combine under one large radical. Answer

Simplify each expression. Rationalize the denominator by multiplying by the same factor. Answer

Simplify each expression. Rationalize the denominator Answer

Simplify each expression. This time, to rationalize the denominator you will need to use two more factors of 3. Answer

Simplify each expression. This time, to rationalize the denominator you should factor the 4. How many more factors of what number will you need? Answer

To simplify a radical by adding or subtracting you must have like terms. Radicals are “like terms” when the indices AND radicand are the same.

Here is an example that we will do together. Rewrite using factors Combine like terms

Try this one on your own.

You can add or subtract radicals like monomials You can add or subtract radicals like monomials. You can also simplify radicals by using the FOIL method of multiplying binomials. Let us try one.

Since there are no like terms, you can not combine.

Lets do another one.

When there is a binomial with a radical in the denominator of a fraction, you find the conjugate and multiply. This gives a rational denominator.

Simplify: Multiply by the conjugate. FOIL numerator and denominator. Next

Combine like terms Try this on your own:

Here are a mixed set of problems to do.

Answers to the mixed set of problems.