Holt Algebra 1

11-6 Radical Expressions11-6 Radical Expressions

Holt Algebra 1

Warm UpWarm Up

Lesson PresentationLesson Presentation

Lesson QuizLesson Quiz

Holt Algebra 1

11-6 Radical Expressions

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

196

25

256

Holt Algebra 1

11-6 Radical Expressions

Warm Up Continued

Write each number as a product of prime numbers.

5. 36

6. 64

7. 196

8. 24

Holt Algebra 1

11-6 Radical Expressions

Simplify radical expressions.

Objective

Holt Algebra 1

11-6 Radical Expressions

Radical expressionRadicandPerfect square

Vocabulary

Holt Algebra 1

11-6 Radical Expressions

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.

Holt Algebra 1

11-6 Radical Expressions

Holt Algebra 1

11-6 Radical Expressions

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.

Holt Algebra 1

11-6 Radical Expressions

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.

Holt Algebra 1

11-6 Radical Expressions

Simplify each radical expression.

Holt Algebra 1

11-6 Radical Expressions

Simplify each radical expression.

Holt Algebra 1

11-6 Radical Expressions

Lesson Quiz: Part I

Simplify each expression.

1.

2.

Simplify. All variables represent nonnegative numbers.

3. 4.

5. 6.

6

|x + 5|

Holt Algebra 1

11-6 Radical Expressions

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