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Today:
Warm-Up: Review Quadratic Formula
Class Work: Simplifying Radicals
April 29, 2013
Notes:
Make Up Tests From Friday?STAR Math Make Up this
WeekReport Card Day This
Thursday
Warm Up/Review:
Warm Up/Review:
Warm Up/Review:
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.
Simplifying Radicals:
Simplifying Radicals:
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.
Example 1: Simplifying Square-Root Expressions
Simplify each expression.
B.A. C.
Example 1
Simplify each expression.
a. b.
Example 1
Simplify each expression.
c.d.
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.
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, .
Example 2a
Simplify. All variables represent nonnegative numbers.
Factor the radicand using perfect squares.
Product Property of Square Roots.
Simplify.
Example 2b
Simplify. All variables represent nonnegative numbers.
Product Property of Square Roots.
Product Property of Square Roots.
Since y is nonnegative, .
Example 2c
Simplify. All variables represent nonnegative numbers.
Product Property of Square Roots.
Factor the radicand using perfect squares.
Simplify.
Simplifying Radicals:
1. 2√21 2. 3√10 3. 5|x|√5
Class Work:
Today:
Warm-Up: Review Quadratic Formula
Class Work: Simplifying Radicals
April 30, 2013
Example 3: Using the Quotient Property of Square Roots
Simplify. All variables represent nonnegative numbers.
Quotient Property of Square Roots.
Simplify.
Simplify.
Quotient Property of Square Roots.
Simplify.
A.B.
Example 3
Simplify. All variables represent nonnegative numbers.
Simplify.
Simplify.
Quotient Property of Square Roots.
Quotient Property of Square Roots.
Simplify.
a. b.
Example 3c
Simplify. All variables represent nonnegative numbers.
Quotient Property of Square Roots.
Factor the radicand using perfect squares.
Simplify.
Example 4A: Using the Product and Quotient Properties Together
Simplify. All variables represent nonnegative numbers.
Quotient Property.
Write 108 as 36(3).
Product Property.
Simplify.
Example 4B: Using the Product and Quotient Properties Together
Simplify. All variables represent nonnegative numbers.
Quotient Property.
Product Property.
Simplify.
Example 4a
Simplify. All variables represent nonnegative numbers.
Quotient Property.
Write 20 as 4(5).Product Property.
Simplify.
Example 4b
Simplify. All variables represent nonnegative numbers.
Quotient Property.
Product Property.
Simplify.Write as .
Example 4c
Simplify. All variables represent nonnegative numbers.
Quotient Property.
Simplify.
Lesson Quiz: Part I
Simplify each expression.
1.
2.
Simplify. All variables represent nonnegative numbers.
3. 4.
5. 6.
6
|x + 5|
Simplifying Radicals:
1.
2.
3.
4.
5.
6.
7.
7. 3/x2
√2x
Class Work:
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
Example 5 Continued
Solve for c.
Substitute 250 for a and b.
Simplify.
Factor 125,000 using perfect squares.
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.
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.
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.
Solve for c.
Substitute 60 for a and b.
Simplify.
Factor 7,200 using perfect squares.
Check It Out! Example 5 Continued
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.
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
Simplifying Radicals:
Simplifying Radicals: