Module 11 Topic 3 Operations with Radical Expressions North Carolina Standard Course of Study Goal 1: The learner will perform operations with numbers and expressions to solve problems. Objective 1.01: Write equivalent forms of algebraic expressions to solve problems.

so You should know the squares of the numbers 1 through 20 to make your life easier.

Example 1 Simplify Remember that you need to simplify all square roots to simplest form. So let’s take each square root and simplify it before adding and subtracting. is in simplest form Now you need to combine like terms (same radicals). break down

Simplify Example 2 Write this out twice. Now add your outer and inner terms. Now use FOIL which is a form of the Distributive Property! First Terms: Outer Terms: Inner Terms: Last Terms: so we have so combine like terms

Example 3 Remember that to find the perimeter of a square you need to add all the sides together. Perimeter = Find the perimeter of a square whose sides have a length of

Example 4 The Butler and Randolph families are swimming in the ocean. The Butler’s leave the starting point, (which is the pier), and swim 3 km East and 5 km South. The Randolph’s leave the starting point and swim 4 km West and 6 km North. How far apart are the two families? (use the distance formula) Remember 3 km East is positive 3 and 5 km South is negative 5. (3, -5) 4 km West is negative 4 and 6 km North is positive 6. (- 4, 6) Remember that the distance formula is