Transcript radical expression
11-6 Radical Expressions Warm Up Identify the perfect square in each set.
1. 45 81 27 111 81 2. 156 99 8 25 25 3. 256 84 12 1000 256 4. 35 216 196 72 196
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11-6 Radical Expressions Warm Up Continued Write each number as a product of prime numbers.
5. 36 6. 64 7. 196 8. 24
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11-6 Radical Expressions
Objective
Simplify radical expressions.
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11-6 Radical Expressions
Vocabulary
radical expression radicand
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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.
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11-6 Radical Expressions Holt Algebra 1
11-6 Radical Expressions
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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11-6 Radical Expressions Example 1: Simplifying Square-Root Expressions Simplify each expression.
A.
B.
C.
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11-6 Radical Expressions Check It Out!
Example 1 Simplify each expression.
a.
b.
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11-6 Radical Expressions Check It Out!
Example 1 Simplify each expression.
c.
d.
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11-6 Radical Expressions Holt Algebra 1
11-6 Radical Expressions 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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11-6 Radical Expressions Example 2B: Using the Product Property of Square Roots Simplify. All variables represent nonnegative numbers.
Product Property of Square Roots.
Product Property of Square Roots.
Since x is nonnegative, .
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11-6 Radical Expressions Check It Out!
Example 2a Simplify. All variables represent nonnegative numbers.
Factor the radicand using perfect squares.
Product Property of Square Roots.
Simplify.
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11-6 Radical Expressions Check It Out!
Example 2b Simplify. All variables represent nonnegative numbers.
Product Property of Square Roots.
Product Property of Square Roots.
Since y is nonnegative, .
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11-6 Radical Expressions Check It Out!
Example 2c Simplify. All variables represent nonnegative numbers.
Factor the radicand using perfect squares.
Product Property of Square Roots.
Simplify.
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11-6 Radical Expressions Holt Algebra 1
11-6 Radical Expressions Example 3: Using the Quotient Property of Square Roots Simplify. All variables represent nonnegative numbers.
A.
B.
Quotient Property of Square Roots.
Simplify.
Simplify.
Quotient Property of Square Roots.
Simplify.
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11-6 Radical Expressions Check It Out!
Example 3 Simplify. All variables represent nonnegative numbers.
a.
b.
Simplify.
Quotient Property of Square Roots.
Simplify.
Quotient Property of Square Roots.
Simplify.
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11-6 Radical Expressions Check It Out!
Example 3c Simplify. All variables represent nonnegative numbers.
Quotient Property of Square Roots.
Factor the radicand using perfect squares.
Simplify.
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11-6 Radical Expressions Example 4A: Using the Product and Quotient Properties Together Simplify. All variables represent nonnegative numbers.
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Quotient Property.
Write 108 as 36(3).
Product Property.
Simplify.
11-6 Radical Expressions Example 4B: Using the Product and Quotient Properties Together Simplify. All variables represent nonnegative numbers.
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Quotient Property.
Product Property.
Simplify.
11-6 Radical Expressions Check It Out!
Example 4a Simplify. All variables represent nonnegative numbers.
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Quotient Property.
Write 20 as 4(5).
Product Property.
Simplify.
11-6 Radical Expressions Check It Out!
Example 4b Simplify. All variables represent nonnegative numbers.
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Quotient Property.
Write as .
Product Property.
Simplify.
11-6 Radical Expressions Check It Out!
Example 4c Simplify. All variables represent nonnegative numbers.
Quotient Property.
Simplify.
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11-6 Radical Expressions 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.
Quadrangle 250
The distance from one corner of the square to the opposite one is the hypotenuse of a right triangle. Use the Pythagorean Theorem: c 2 = a 2 + b 2 .
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11-6 Radical Expressions Example 5 Continued
Solve for c.
Substitute 250 for a and b.
Simplify.
Factor 125,000 using perfect squares.
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11-6 Radical Expressions Example 5 Continued
Use the Product Property of Square Roots.
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Simplify.
Use a calculator and round to the nearest tenth.
The distance is ft, or about 353.6 feet.
11-6 Radical Expressions Check It Out!
Example 5 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.
The distance from one corner of the square to the opposite one is the hypotenuse of a right triangle. Use the Pythagorean Theorem: c 2 = a 2 + b 2 .
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11-6 Radical Expressions Check It Out!
Example 5 Continued
Solve for c.
Substitute 60 for a and b.
Simplify.
Factor 7,200 using perfect squares.
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11-6 Radical Expressions Check It Out!
Example 5 Continued
Use the Product Property of Square Roots.
Simplify.
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Use a calculator and round to the nearest tenth.
The distance is , or about 84.9 feet.
11-6 Radical Expressions Lesson Quiz: Part I Simplify each expression.
1.
6
2.
|x + 5|
Simplify. All variables represent nonnegative numbers.
3.
4.
5.
6.
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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
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