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Pg. 122 from Student Journal Complete 1-13

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1 Pg. 122 from Student Journal Complete 1-13
Bellwork Pg. 122 from Student Journal Complete 1-13 Algebra II

2 Bellwork Problems Algebra II

3 Bellwork Problems cont..
Algebra II

4 BW cont… Algebra II

5 nth Roots and Rational Exponents
5.1 nth Roots and Rational Exponents Algebra II

6 “the nth root of x to the mth”
Vocabulary Pg. 125 SJ exponent index exponent base radicand “x to the nth power” “the nth root of x to the mth” Algebra II

7 State the index and the radicand for each. SJ Pg. 125
*an index of 2 is understood if one is not written 1. √ √ √ √p index: 2 radicand: 10 index: 3 radicand: 81 index: 7 radicand: 92 index: 4 radicand: p Algebra II

8 Rational Exponent Rules SJ Pg. 126
Algebra II

9 Write each using rational exponents. SJ Pg. 126 (Notes)
1. √x = 2. 3√y2 = 3. 8√52 = 4. 4√95 = x ½ y 2/3 5 2/8 = 5 1/4 9 5/4 Algebra II

10 Write each using radicals. SJ pg. 126 (Notes)
1. 3 2/9 = /10 = /3 = 4. x 9/4 = 9√32 10√43 3√62 4√x9 Algebra II

11 SJ Pg. 127: Matching Algebra II

12 Simplifying nth Radicals
Square Roots 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144… Cube Roots 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000… Fourth Roots 1, 16, 81, 256, 625, 1296… Fifth Roots 1, 32, 243, 1024, 3125… Algebra II

13 Find each without a calculator
1. 3√-125 = 2. 4√16 = 3. 5√-32 = 4. 3√27 = 5. 93/2 = /5 = /2 = /3 = -5 2√93 = 33 = 27 1 = = 1 5√ 2 -2 2√165 = 45 3 1 = = 1 3√ Algebra II

14 Student Journal Pg. 124 Evaluate each without a calculator. Algebra II

15 Student Journal Pg. 126 Evaluate each without a calculator. Algebra II

16 Student Journal Pg. 123 Use a calculator to find each value Algebra II

17 SJ Pg. 125 Algebra II

18 Solve each using nth roots: real answers only.
1. 2x4 = 162 x4 = 81 4√x4 = 4√81 x = ±3 2. (x – 2)3 = 10 3√(x – 2)3 = 3√10 x – 2 = 3√10 x = 2 + 3√10 Only put a ± when the index is even! Algebra II

19 Solve each using nth roots: real answers only.
3. 2(y - 1)5 = -64 (y – 1)5 = -32 5√(y – 1)5 = 5√-32 y – 1 = -2 y = 1 – 2 y = -1 4. 2(x + 1)2 = 72 (x + 1)2 = 36 2√(x + 1)2 = 2√36 x + 1 = ± 6 x = -1 ± 6 x = -1+6 x = -1-6 x = 5 x = -7 Only put a ± when the index is even! Algebra II

20 SJ Pg. 127: 16-19 Algebra II

21 SJ Pg. 127 Algebra II

22 Simplifying nth Radicals
Square Roots 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144… Cube Roots 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000… Fourth Roots 1, 16, 81, 256, 625, 1296… Fifth Roots 1, 32, 243, 1024, 3125… Algebra II

23 Simplify each. 1. 3√54 2. 4√64 Cube Roots: 1,8,27,64,125,216,343
1. 3√54 Cube Roots: 1,8,27,64,125,216,343 3√54 = 3√27∙2 = 3√27∙3√2 = 33√2 2. 4√64 Fourth Roots 1,16,81,256 4√64 = 4√16∙4√4 = 2 4√4 Algebra II

24 Simplify each. 3. 3√48 4. 4√162 Cube Roots: 1,8,27,64,125,216,343
3. 3√48 Cube Roots: 1,8,27,64,125,216,343 3√48 = 3√8∙6 = 3√8∙3√6 = 23√6 4. 4√162 Fourth Roots 1,16,81,256 4√162 = 4√81∙4√2 = 3 4√2 Algebra II

25 Manipulative Activity
Algebra II

26 Simplify each. 5. 3√250y7 6. 3√125∙2∙y7 5y2 3√2y Cube Roots:
1,8,27,64,125,216,343 3√125∙2∙y7 5y2 3√2y 6. Algebra II

27 Simplify each. 7. 3√81z5 8. 4√162x9 3√81z5 = 3√27∙3∙z5 = 3z 3√3z2
Cube Roots: 1,8,27,64,125,216,343 3√81z5 = 3√27∙3∙z5 = 3z 3√3z2 8. 4√162x9 Fourth Roots 1,16,81,256 4√162x9 = 4√81∙2∙x9 = 3x2 4√2x Algebra II

28 Simplify each. 9. 3√56x3z5 10. 4√48x12y15 3√8·7x3z5 = 2xz 3√7z2
Cube Roots: 1,8,27,64,125,216,343 3√8·7x3z5 = 2xz 3√7z2 10. 4√48x12y15 Fourth Roots 1,16,81,256 4√48x12y15= 4√16∙3x12y15 = 2x3y3 4√3y3 Algebra II

29 Application Problems 1. The equation to estimate wind chill temperature C, for an air temperature of 5° F and a wind speed of s miles per hour is C = 69.2(0.94s) – 50. What would the windchill temperature be if the wind speed is 20 mph. Algebra II

30 Application Problems 2. The shot used in men's shot put has a volume of about 905 cubic centimeters. Find the radius of the shot. Round to the nearest hundredth. (Hint: Use the Formula V= 4/3πr3) Algebra II

31 Application Problems Algebra II

32 Application Problems Algebra II

33 Closure: Exit Pass 1, 5 Algebra II


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