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