12.2 Operations with Radical Expressions √ Algebra 12.2 Operations with Radical Expressions √

Review: Simplifying √ Expressions Prime factorization can be useful 1. Factor terms under the radical. Find the largest perfect square factor(s). Take square roots outside. 2. Rewrite in simplified form.

Warm-Up: You try.

Adding and Subtracting Radicals You can add and subtract terms that have the same radicand. These are LIKE TERMS.

Add and Subtract: You try. Simplify each radical term first

Add and Subtract: Simplify each term first.

Multiplying Radicals 1. Multiply terms outside the radical together. 2. Multiply terms inside the radical together. 3. Simplify.

Multiplying Radicals You can multiply using distributive property and FOIL. It’s a DTS!

Multiply: You try. It’s a PST!

Dividing to Simplify Radicals No radicals in the denominator allowed Denominators must be “rationalized.” √ Multiply by 1in the form of √ 3 1

Using the Conjugate to Simplify The other part of a DTS Expression Conjugate Product The radical “goes away” every time

Dividing to Simplify Radicals conjugate Multiply by 1in the form of conjugate 5 1 11

Simplify: You try.

Summary: To ADD and SUBTRACT To MULTIPLY To DIVIDE COMBINE LIKE TERMS “Outside” NUMBERS x NUMBERS “Inside” NUMBERS x NUMBERS DISTRIBUTE and FOIL To DIVIDE “Rationalize” denominator using 1 Use conjugate ALWAYS SIMPLIFY AT THE END IF YOU CAN