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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

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Warm Up Continued

Write each number as a product of prime numbers.

5. 36

6. 64

7. 196

8. 24

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Simplify radical expressions.

Objective

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radical expressionradicand

Vocabulary

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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.

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Remember that positive numbers have two square roots, one positive and one negative. However, indicates a nonnegative square root. When you simplify, be sure that your answer is not negative. To simplify you should write because you do not know whether x is positive or negative.

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Example 1: Simplifying Square-Root Expressions

Simplify each expression.

B.A. C.

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Check It Out! Example 1


a. b.

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c. d.

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Example 2A: Using the Product Property of Square Roots

Simplify. All variables represent nonnegative numbers.

Factor the radicand using perfect squares.

Product Property of Square Roots.

Simplify.

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Example 2B: Using the Product Property of Square Roots




Since x is nonnegative, .

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Check It Out! Example 2a




Simplify.

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Check It Out! Example 2b




Since y is nonnegative, .

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Check It Out! Example 2c




Simplify.

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Example 3: Using the Quotient Property of Square Roots


Quotient Property of Square Roots.

Simplify.

Simplify.


Simplify.

A. B.

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Simplify.

Simplify.



Simplify.

a. b.

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Simplify.

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Example 4A: Using the Product and Quotient Properties Together


Quotient Property.

Write 108 as 36(3).

Product Property.

Simplify.

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Example 4B: Using the Product and Quotient Properties Together


Quotient Property.

Product Property.

Simplify.

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Check It Out! Example 4a


Quotient Property.

Write 20 as 4(5).

Product Property.

Simplify.

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Check It Out! Example 4b


Quotient Property. Product Property.

Simplify.Write as .

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Quotient Property.

Simplify.

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Example 5: Application

A quadrangle on a college campus is a square with sides of 250 feet. If a student takes a shortcut by walking diagonally across the quadrangle, how far does he walk? Give the answer as a radical expression in simplest form. Then estimate the length to the nearest tenth of a foot.

The distance from one corner of the square to the opposite one is the hypotenuse of a right triangle. Use the Pythagorean Theorem: c2 = a2 + b2.

250

250

Quadrangle

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Example 5 Continued

Solve for c.

Substitute 250 for a and b.

Simplify.

Factor 125,000 using perfect squares.

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Example 5 Continued

Use the Product Property of Square Roots.

Simplify.

Use a calculator and round to the nearest tenth.

The distance is ft, or about 353.6 feet.

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A softball diamond is a square with sides of 60 feet. How long is a throw from third base to first base in softball? Give the answer as a radical expression in simplest form. Then estimate the length to the nearest tenth of a foot.

60

60

The distance from one corner of the square to the opposite one is the hypotenuse of a right triangle. Use the Pythagorean Theorem: c2 = a2 + b2.

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Solve for c.

Substitute 60 for a and b.

Simplify.

Factor 7,200 using perfect squares.

Check It Out! Example 5 Continued

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Use the Product Property of Square Roots.

Simplify.

Use a calculator and round to the nearest tenth.

Check It Out! Example 5 Continued

The distance is , or about 84.9 feet.

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Lesson Quiz: Part I


1.

2.


3. 4.

5. 6.

6

|x + 5|

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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

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