Simplifying Radical Expressions

Warm Up: Simplify

Here are the answers:

Essential Question: When is a radical expression completely simplified?

The radicand contains no fractions. Essential Question: When is a radical expression completely simplified? 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.

Essential Question: What are like radicals?

To add or subtract radical expressions you must have “like radicals”. Like radicals are when the index AND radicand are the same.

Essential Question: How can you add and subtract radicals? Simplify all radicals if you can. Combine radicals Complete #1-6 on WS

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

RADICAL EXPRESSIONS EX-adding RULES Have to have same number on inside Have to have same index

RADICAL EXPRESSIONS EX-adding

Try this one on your own.

How can I multiply binomial radical expressions?

You can multiply binomial radical expressions 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.

Essential Question: -How can you rationalize a radical out of the denominator? -What is a conjugate?

Review - RATIONALIZING a DENOMINATOR How to rationalize using conjugates If there is a radical in the bottom, then you must rationalize it.

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.