1 / 10

Section 7.1

Section 7.1. Roots and Radical Expressions. Write each number as a square of a number. 1. 25 2. 0.09 3. Write each expression as a square of an expression. 4. x 10 5. x 4 y 2 6. 169 x 6 y 12. 4 49. Roots and Radical Expressions. ALGEBRA 2 LESSON 7-1. (For help, go to Lesson 5-4.).

dane-neal
Télécharger la présentation

Section 7.1

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Section 7.1 Roots and Radical Expressions

  2. Write each number as a square of a number. 1. 25 2. 0.09 3. Write each expression as a square of an expression. 4.x105.x4y26. 169x6y12 4 49 Roots and Radical Expressions ALGEBRA 2 LESSON 7-1 (For help, go to Lesson 5-4.) Check Skills You’ll Need 7-1

  3. 1. 25 = 522. 0.09 = 0.323. = = 2 4.x10 = (x5)25.x4y2 = (x2y)26. 169x6y12 = (13x3y6)2 4 49 22 72 2 7 Roots and Radical Expressions ALGEBRA 2 LESSON 7-1 Solutions 7-1

  4. 1 64 1 64 1 64 a. the cube root of 0.027, –125, and 1 4 1 4 Since 3 = , is the cube root of . 81 625 81 625 81 625 81 625 b. the fourth roots of 625, –0.0016, and –3 5 3 5 3 5 3 5 Since 4 = and 4 = , and – are fourth roots of . Roots and Radical Expressions ALGEBRA 2 LESSON 7-1 Quick Check Find all the real roots. Since 0.33 = 0.027, 0.3 is the cube root of 0.027. Since (–5)3 = –125, –5 is the cube root of –125. Since 54 = 625 and (–5)4 = 625, 5 and –5 are fourth roots of 625. There is no real number with a fourth power of –0.0016. 7-1

  5. a. –1000 Rewrite –1000 as the third power of a number. 3 Definition of nth root when n = 3, there is only one real cube root. = –10 3 = (–10)3 b. –81 Roots and Radical Expressions ALGEBRA 2 LESSON 7-1 Find each real-number root. There is no real number whose square is –81. Quick Check 7-1

  6. a. 9x10 9x10 =32(x5)2 = (3x5)2 = 3| x5| Absolute value symbols ensure that the root is positive when x is negative. 3 b.a3b3 3 (ab)3 = ab Roots and Radical Expressions ALGEBRA 2 LESSON 7-1 Simplify each radical expression. Absolute value symbols must not be used here. If a or b is negative, then the radicand is negative and the root must also be negative. 7-1

  7. c.x16y4 4 x16y4 = (x4)4(y)4 = x4 |y| 4 4 Roots and Radical Expressions ALGEBRA 2 LESSON 7-1 (continued) Absolute value symbols ensure that root is positive when y is negative. They are not needed for x because x4 is never negative. Quick Check 7-1

  8. < < < < < < < < < < – – – – – – – – – – 10 w 11 Write an inequality. d3 5 10 11 Substitute for w in terms of d. 50 d3 55 Multiply by 5. d3 5 50 d3 55 Take cube roots. 3 3 3 3.68 d 3.80 The diameters range from 3.68 in. to 3.80 in. Roots and Radical Expressions ALGEBRA 2 LESSON 7-1 A cheese manufacturer wants to ship cheese balls that weigh from 10 to 11 ounces in cartons that will have 3 layers of 3 cheese balls by 4 cheese balls. The weight of a cheese ball is related to its diameter by the formula w = , where d is the diameter in inches and w is the weight in ounces. What size cartons should be used? Assume whole-inch dimensions. Find the diameter of the cheese balls. 7-1

  9. Roots and Radical Expressions ALGEBRA 2 LESSON 7-1 (continued) The length of a row of 4 of the largest cheese balls is 4(3.80 in.) = 15.2 in. The length of a row of 3 of the largest cheese balls 3(3.80 in.) = 11.4 in. The manufacturer should order cartons that are 16 in. long by 12 in. wide by 12 in. high to accommodate three dozen of the largest cheese balls. Quick Check 7-1

  10. 3 4 3 1 25 1 216 Roots and Radical Expressions ALGEBRA 2 LESSON 7-1 1. Find all the real square roots of each number. a. 121 b. –49 c. 64 d. – 2. Find all the real cube roots of each number. a. –8000 b. 3. Find each real-number root. a. 0.49 b. 125 c. – 81 d. –625 4. Simplify each radical expression. a. –8x3b. 16y4c. 36x14 5. The formula for the volume of a cone with a base of radius r and height r is V = r 3. Find the radius to the nearest hundredth of a centimeter if the volume is 40 cm3. ± 11 none ± 8 none 1 6 –20 5 –9 0.7 none 6 | x7 | 4y2 –2x 1 3 about 3.37 cm 7-1

More Related