11-6 Radical Expressions Warm Up Lesson Presentation Lesson Quiz Holt Algebra 1

Warm Up Identify the perfect square in each set. 1. 45 81 27 111 2. 156 99 8 25 3. 256 84 12 1000 4. 35 216 196 72 81 25 256 196

Warm Up Continued Write each number as a product of prime numbers. 5. 36 6. 64 7. 196 8. 24

Objective Simplify radical expressions.

Vocabulary Radical expression Radicand Perfect square

An expression that contains a radical sign is a radical expression An expression that contains a radical sign is a radical expression. There are many different types of radical expressions, but in this course, you will only study radical expressions that contain square roots. Examples of radical expressions: The expression under a radical sign is the radicand. A radicand may contain numbers, variables, or both. It may contain one term or more than one term.

The First 20 Perfect Squares A perfect square is a number whose square root is a whole number. It will be beneficial in the throughout upper level math to know common perfect squares.

There are two common methods of removing perfect squares from the radicand.     Method 1: Divide all perfect square factors from the radicand. Method 1: Break down the radicand into product of primes. Then remove any pairs from the radical.

Simplify each radical expression.      

  Simplify each radical expression.

Lesson Quiz: Part I Simplify each expression. 1. 6 2. |x + 5| Simplify. All variables represent nonnegative numbers. 3. 4. 5. 6.

Lesson Quiz: Part II 7. Two archaeologists leave from the same campsite. One travels 10 miles due north and the other travels 6 miles due west. How far apart are the archaeologists? Give the answer as a radical expression in simplest form. Then estimate the distance to the nearest tenth of a mile. mi; 11.7mi