Unit 3- Radical Expressions I. Simplifying Radicals

A. What is a radical? 1) Notation Radical sign Radicand

4) Simplifying Radicals

Try on your own Simplify the following radicals: 1) 2) ANSWER ANSWER

Look for factors of of 48 that are perfect squares. B. What if the expression under the radical isn’t a perfect square? Method 1 Look for factors of of 48 that are perfect squares. Example 1: Simplify the following radical: Notice that we factored 48 into 16 and 3. We chose this factorization because 16 is a perfect square and equals 4

Example 1: Method 2 Use Prime Factorization! What is the prime factorization of 48? 48 24 2 2 12 6 2 2 3

Now, circle pairs of factors that are the same. Why pairs?! Because the index is two for square roots! For each pair, pull out one of those factors and place it in front of the radical

A Visual Representation of Simplifying Radicals

Try on your own: Simplify the following radical Method 2 Method 1 HINT HINT ANSWER ANSWER

Example 2 Simplify the following Radical: Method 1 Look for perfect squares under the radical

Example 2: Method 2 Write out all factors of the expressions under the radicals (the prime factorization)

Try on your own: Simplify the following Radical Method 1 Method 2 HINT HINT ANSWER ANSWER

Example 3: Method 1 Simplify the following radical:

Example 3 Method 2 Write out all factors of the radicand (its prime factorization)

Try on your own: Simplify the following radical: Method 1 Method 2 HINT HINT ANSWER ANSWER